Harrowed Spellstrike specifies that the range of the spell is changed to the range increment of the thrown weapon. Because 'Touch' is unfortunately a range increment, this means according to the book rules you need to make a ranged attack (not a ranged touch attack) with your cards for the spell to work. That sucks. This is also true of the regular Spellstrike ability, but that ability specifically replaces the touch attack granted by casting a touch range spell rather than the range of the spell itself. The base Spellstrike, then, allows its user to Hold the Charge (a property of the touch range), while the Harrowed Spellstrike does not and, in fact, loses all benefits of the Touch range.
However, you're in luck! The designers, addressing ill-founded concern over a magus's ability to use spellstrike at all (concern which clearly does not draw basis from the RAW) posted this:
Basically, the spellstrike gives the magus more options when it comes to delivering touch spells; it’s not supposed to make it more difficult for the magus to use touch spells.
Sean K Reynolds
Designer
This gives you some ground in trying to talk your GM into making Harrowed Spellstrike better in some way.
Yes, this build is competitive. Compared with a strength based dueling paladin, you'll actually be better off in many ways. Though you can't compete with a great weapon fighting paladin in damage. To illustrate this: let's compare some general build options.
Let's assume there are two paladins: Strong and Dexter. Strong and Dexter have the same stats except that Dexter has dexterity equal to Strong's strength, and strength equal to Strong's dexterity. This means that for the purposes of attack rolls and damage modifiers, the two are exactly the same. For that reason, I'm omitting modifiers when I make damage assessments below. I'm also not including magic items because with enough magic, you can make anything work.
Sword and Board
Dexterity is very competitive here, if not the best choice. In this case, both paladins take the dueling style and wield a weapon in one hand and a shield in the other. The highest damage one handed weapons all deal 1d8 damage. For Dexter, that means using a rapier. For Strong, it could be a longsword, warhammer, battleaxe, or rapier. Regardless, because the damage die is the same, and the paladin's relevant ability score modifiers are the same, their damage output is identical. Eventually, when Strong gets plate armor, they will have 1 higher AC than Dexter does (18+2 vs 17+2, as you have noted) Strong also has options to deal all three types of physical damage (slashing, bludgeoning, and piercing). Dexter will only be able to deal piercing damage, but their initiative, stealth, and dexterity saves will all be higher than Strong's. Dexter also has much better ranged attack options since they're as effective with a bow as with their rapier.
In return for being 5% easier to hit compared to Strong with plate armor, Dexter will be better at range, go earlier in the initiative more often, and make their dexterity saving throws more often than Strong does. Honestly, that's a pretty fair trade off.
Great Weapon Fighting
Dexter can't compete with Strong's damage here. Dexter keeps their shield and rapier. But Strong takes great weapon fighting and a heavy weapon. Their damage die goes up to either 1d12 or 2d6, depending on which weapon they choose. And they get to reroll 1s and 2s on that damage. Using the results of the How much damage does Great Weapon Fighting add on average question, that works out to roughly an extra +1 damage on average. So, strong will be dealing about 8 damage per hit before modifiers regardless of which weapon they choose. Strong could also take the Great Weapon Master (GWM) feat to further increase their damage output. Dexter is still dealing about 4.5 per hit before modifiers with their rapier and doesn't really have any feats that will consistently increase their damage to Strong's level. So, Strong is dealing twice as much damage as Dexter on average. However, Strong loses their shield. So even with plate armor, Dexter now has a 1 AC advantage (17+2 vs 18), making them 5% harder to hit than Strong. And Dexter is still better at initiative, ranged attacks, and dexterity saving throws.
Two-Weapon Fighting
Here's an interesting option. If Dexter has 13 strength, they can take one level of fighter to pick up the two-weapon-fighting style. They also take the Dual wielder feat so they can use two rapiers. Now, Dexter and Strong have the same AC (17+1 vs 18) and Dexter deals an extra 4.5 damage on average with their off hand attack. up until 4th level, Strong will deal about 8 damage per hit and Dexter will deal about 9 damage over two hits. So Dexter hits harder than Strong! As long as both attacks hit anyway.
The issue is that once the paladins hit 5th level they get an extra attack. Strong now deals 16 damage over two hits (8 damage twice), and Dexter deals 13.5 damage over three hits (4.5 damage thrice). And that doesn't factor in the bonus damage that GWM offers Strong. At this point, Strong hits harder than Dexter does, and again Dexter can't do much to catch up.
Final Thoughts
This is a very quick analysis. Enough to get the point across I think. There is no way for a Paladin using dexterity to deal the same damage as a paladin that's focusing on dealing as much weapon damage as possible. If you want to deal maximum damage, you have to go with a strength paladin. But dexterity gives you much better survivability. Dexterity saving throws are very common, and can deal some really high damage (think fireballs, lightning bolts, and fiery dragon breath). And with higher dexterity you can go earlier in the initiative and position yourself where you need to be as soon as possible. Plus the large damage bursts that paladins are known for because of their smite is, as you have pointed out, not dependent on weapon damage. It's just based on spell slot level. All of that is to say, the survivability and flexibility is something that will definitely serve you well and I personally think is a reasonable trade-off.
Best Answer
The advantage of a Strength-based magus is that it avoids some of the disadvantages of a Dexterity-based magus. The disadvantage is that it also misses out on the advantages of a Dexterity-based magus. This is tautological, but I introduce things this way because Strength is the default, and aside from being the default and therefore not requiring any investment, Strength has no real advantages for a magus. After all, a magus cannot use a two-handed weapon,1 which is the only real way to make Strength shine.
So then, the disadvantage of being Dexterity-based is that you have to expend character-creation resources in order to become Dexterity-based, i.e. take the Weapon Finesse feat. Once you have taken the Weapon Finesse feat, your weapon damage is poor, since you are doing this to dump Strength. Shocking grasp arguably says you don’t care, but if you do, that means you also take Dervish Dance,2 Fencing Grace,2 or Slashing Grace,2 or wield an agile weapon.
So the Dexterity-based magus is down a feat and a +1-enhancement equivalent on their weapon, or down two feats. Assuming you don’t lose your weapon, the weapon route is the better deal, but you would have to judge that risk yourself—and a bladebound magus, obnoxiously, wouldn’t have the option. What do you get for your expense?
You will be more accurate, and if you get Dexterity-to-damage, you will also deal more damage. That is, your Dexterity will be higher than your Strength would be on a Strength-based magus, because you can completely ignore Strength while a Strength-based magus really should have at least decent Dexterity. Without a two-handed weapon, Strength has no advantage to offset this benefit.
Your initiative is much improved. This is huge, because in most combats initiative will easily be the single most important roll you make. They will be decided primarily by who goes first. This becomes especially true at higher levels, where the game becomes increasingly rocket tag.3
You get substantially more AC, to the point that keeping your AC relevant becomes a meaningful, if expensive, option. Most characters at mid-to-high levels cannot afford enough AC to make it worthwhile, and should optimally end up basically ignoring it after the basic bonuses from a +1 armor. A Dexterity-focused character in light armor is just about the only exception.
Your skills will quite simply be better. Climb is worthless once you have flight—which you should—and Swim comes up rarely, if at all, in most campaigns. Meanwhile, Acrobatics and Stealth are two of the best skills in the game.
So, are all of those worth a feat or two? Generally speaking, yes, they are. Feats are very valuable, but that is a lot of benefit. There are not a lot of feats that could offer so much.
That said, there are also some really powerful feats out there. You will have to look at your build and decide if another feat or two could add even more than all of that.
There’s an argument that a magus can use a two-handed weapon—I’ve made it myself, here—but I’m largely going to ignore it on the basis of your request to avoid cheese. It doesn’t really change my conclusions, but it becomes harder to speak definitively in that case.
Unless you are forced to take Weapon Focus for something else, Dervish Dance is the best option here. No weapon option available to you is worth having to burn a feat on Weapon Focus for.
The game is actually most “rocket tag” at 1st level, but that’s irrelevant to the question.