From my experience at jungle with tryndamere, the summoner spells i find most useful are smite and ignite. The reason goes as follows, smite is obviously easier to jungle with, and ignite is also a good jungling tool along with being useful to kill enemy champions later on in the game. Exhaust is a waste with trynd since his Mocking Shout (W) automatically slows the enemy down. Ghost is also a waste since having boots and phantom dancer pretty much makes you faster than anyone else in the game. Flash is just a no, your spinning slash (E) is your flash. Heal, idk why u would get heal for trynd, he has his Q and infinity rage, if u need heal to survive then u shouldn't be playing trynd. Lets see the other summoner spells are clarity and clairvoyance which are pretty much useless for trynd. The tower protect spell (the name has slipped my mind) should be used by your support.
Now that i got the spells out of the way, the items i go with is cloth armor and 4 red potions. You can get 5 but you really dont need the 5th one unless you want to be extra catious. The first thing i do when i jungle is get red lizard with the help of a teamate who should leash it. As long as you get one crit hit on lizard plus the smite and ignite, you should kill it with about 50 health or so. You will need to use a potion imediately after the first hit otherwise you will not survive. The best leashes are when your teamate hit the lizard 3-5 times. This way you will still have half your health and your teamate will also have about 3/4 of their health remaining.
Immediately after lizard i get both golems. Attacking them while using another potion for healing. Smite will still be on cooldown and should not be used while fighting these 2 golems. While fighting the golems it is helpful to hit and slightly run away and occasionaly hit the same golem until the second retreats. This way you essentially only take the damage of one of the golems. Once smite reactivates, take out the wraiths. Spin slash into the wraiths while simultaneously using smite on the blue one. You should easily kill them while gaining health so dont use a potion here. Go to the wolves and kill. Now you can take blue golem. Notice, you will risk dying so do this if you feel comfortable with your trynd skills. Start off by killing both of the minions. Then start attacking the golem. Whenever your rage hits 100 heal. Your smite should reactivate mid fight with golem so use it. From there determine whether you can kill the golem or have to retreat. I end up killing the golem half the time with less than 100 health remaining. Now you can go back to base and get your wrigglers lanterns and a pair of boots.
From here on out i am pretty sure you can figure out what to do.
The order to rank up your abilities are: Q-E-Q-W-Q-R (Then max out your Q and W, with E being maxed out last)
If you have a decsent team then you will easily destroy the opposition since you will be about 1 or 2 levels ahead of everyone.
Tryndamere is one of League of Legend's melee carry-s, which means, indeed, that he becomes nigh-unstoppable lategame as he gets more and more items (though despite what you may think, Tryndamere is not nearly as powerful now as he was back near release)
Tryndamere's counter is hard CC. If you don't have CC (which is quite possible in blind pick), you have no real option other than to prevent him from getting kills in the first place.
This is, in part, why Tryndamere is considered something of a "newbie stomper" - without CC and coordination, both often lacking in newer players, he can be a royal pain to deal with.
The truth of the matter is that Tryndamere, like all carry-s, is fragile. Without his ult, he melts like paper, especially under focus.
What Tryndamere wants you to do, more than anything else, is stand still and let him crit you to death. So don't let him - use your CC to snare him, slow him, keep him at arms length. (I dare say you'd be hard pressed to find a team of 5 without one slow or better betwixt all of them)
The goal when fighting Tryndamere should be to get him to use his ult, then disable him for its duration, then kill him. If he uses his ult to flee, all the better - re-engage on a team fight within 2 minutes, and it'll still be on cooldown, making him prime to focus.
In terms of surviving Tryndamere, you want armor, and lots of it. A Thornmail will cause Tryndamere's massive crits to likewise sliver his own health, while a Frozen Heart will reduce his attack speed while providing you armor (and mana).
Best Answer
Pros:
Makes him stronger in long, drawn out fights since it allows you to fully stack it
Gives him a better 1v1 potential and split-pushing threat, which is pretty much what the champion is all about
Increases your AOE(Area of Effect) in Teamfights or 2v1's
Gives you more waveclear (Same has increasing Split-pushing capability)
Cons:
Doesn't provide you any real stat( You have to Auto-Attack to gain the benefits)
Pretty much only increases what he is already good at(2v1 , split-push threat), at the cost of one item and doesn't cover any of his weaknesses( Heavy CC, being targeted or picked off)
Overall:
While it isn't the worst Item for him, personally i wouldn't do it unless i was really fed already, feel that a Sterak's or Maw would be better to provide you with more survivability in a TeamFight or in a 3v1 situation
Regarding your final Build :
I think you are going a bit too overkill on the Damage, you don't need Essence Reaver or BloodThirster, my personal favorite build for him is:
Blade of the Ruined King, Stattik Shiv, Infinity Edge(if ahead) or Ravenous Hydra( If im going for split push), a Sterak's, and then some Situational Items, if they have lots of CC (Crowd Control), i would go for Mercurial Scimitar, if they have Tanks i would go for a Lord Dominik's Regard, if they have Squish i would go for more damage, all Depends on the comp you are playing agaisnt really
If you really want to replace Guinsoo's onto your final build, just remove Essence Reaver, it doesn't benefit you has much has the Guinsoo, although i don't completely agree with your Overkill damage build, but hey, opinions