Yes.
This may seem overpowered but there are several drawbacks to the spell:
The target's game statistics, including mental ability scores, are
replaced by the statistics of the chosen beast. It retains its
alignment and personality.
If you transform them into a T-Rex they become an unintelligent beast with an INT score of 2.
The creature is limited in the actions it can perform by the nature of
its new form, and it can't speak, cast spells, or take any other
action that requires hands or speech.
It can't communicate with you while in its new form or use its hands to activate any items, or otherwise perform any task that requires hands or speech.
The target's gear melds into the new form. The creature can't
activate, use, wield, or otherwise benefit from any of its equipment.
It's AC changes to 13 (T-Rex is easy to hit but not easy to kill) making it an easy target from long range. It can't benefit from any magic items it might have or any armor or shields.
Also, the spell requires concentration. This carries two more drawbacks.
If the caster takes damage he or she must make a concentration check to maintain concentration. If it fails, the target reverts form which could potentially put them in a very bad situation, surrounded by enemies and perhaps with low HP (maybe polymorph was cast on the fighter when he was almost out of his own HP).
The other drawback here is the opportunity cost of concentration. The caster can't concentrate on any other spells while he is concentrating on polymorph, which means any other spells available to the caster that require concentration aren't available for the duration. This is a spell list that includes things like hold person, fear, suggestion, haste, slow, wall of fire, web, invisibility, greater invisibility, and levitate, to name only a handful of the concentration spells available to a level 7 wizard.
Consider also that beyond class level 7, there would be even more concentration spells available which might come at a higher opportunity cost than polymorph.
Furthermore, there is also the opportunity cost of learning polymorph. When you first gain access to it at level 7 as a wizard or sorcerer, you have 1 (sorcerer, bard) or 2 (wizard) spell choices available. Druid gets it automatically as they know all their spells -- crazy, right?
As a bard or a sorcerer at that level, you have chosen to forgo all other level 4 spells so that you can transform something into a T-Rex for one hour once a day (maybe more if you spend sorcery points). As a wizard, you have a little more flexibility. In any case, the opportunity cost of choosing this spell over any other spell should come with an appropriate value -- in this case, the ability to temporarily transform someone into a powerful beast and the versatility of being able to transform them into any other less powerful beast.
However, I think you're overlooking the more powerful use of polymorph -- the potential of turning any opponent of yours into a harmless chicken or goat while you take care of the rest of the goons trying to steal your gold. Removing a single powerful enemy from combat is a much better use of your action than creating a powerful ally, when creating a T-Rex leaves the powerful enemy on the table to make attacks against you and your other party members.
For background, I run an online session with people spanning an eight hour time difference. Our scheduling is generally a mess and we vary between 45 minute and 4 hour sessions depending on the day. I've picked up a few tricks to help things move more smoothly.
Plan ahead
A lot of time in-game is spent having either in- or out-of-character discussions about what your next move is going to be. Encourage your players to discuss their options outside of your games (maybe set up a chat or text group between them all) so they walk into each session with a plan ready to go, and only have to spend three minutes explaining it to you instead of thirty five figuring it out.
Get buy-in
Your players should be aware of the time crunch as keenly as you are. Ask for some small sacrifices in their play styles to make the whole game go more smoothly. Maybe your sorcerer needs to study his spells for a couple days until he can make snap decisions on the fly, or your fighter could use flashcards so she knows what attacks she can make.
Basically, encourage your players to find shortcuts in how they play to match the shortcuts you'll be taking. This kind of ties into the plan ahead step above, but is more about players knowing what they can and can't do like the back of their hands.
Be prepared to end early
I've learned to spot good (and sometimes just decent) stopping points and grab them, even if it is a little earlier than our time slot should be ending. Better to end on a high note than get interrupted in the middle of a good scene.
For example, if you're about to infiltrate a hideout and you only have 5mins left in your lunch period, call it quits before they start to enter. No point getting halfway down the first hallway just to have to pause, and you can use the extra five minutes to have them plan their angle of attack for tomorrow instead.
Fudge it
If you know you only have 10 minutes left and they're mid-boss-fight, there's no harm in quietly knocking off 10% of the big baddie's health, or letting him go down if one of your players manages a particularly spectacular roll.
Similarly, you can always have minions escape instead of fighting to the last drop of HP. It's easy to shave a minute or two off your play time just by making the world bend to your PC's wishes. Done carefully and silently enough, they won't even notice that you're fudging things.
Recap early
If your sessions are anything like mine, you'll spend at least five minutes at the beginning recapping what happened last time and fielding questions from your less attentive players. Move this process away from the table and you'll get your five minutes back.
Take a bit of time after each session to write up a couple sentences about what happened, and post it to your group chat. Then your players can read up on it before they get to the table and you can skip the live recap.
Skip the lines; shop online
Some groups may love to roleplay the shopping experience, but if your party is in the take it or leave it camp, this can be a great way to save time. Instead of painstakingly letting each player play through buying / selling / identifying everything each time they hit a town, end the session and take the deals online.
Try to time your shopping sprees to start at the end of your session, then tell everyone to text you their to-do lists. You can work through them one-on-one and get everyone squared away before the next session.
Now this requires two things; they need to trust you'll do right by them, and because of that sometimes you'll need to just say yes. If they say they'd barter for the potion, give them a (reasonable) discount. If they're trying to find a specific type of mirror, agree that they've found it (unless you have really good reason not to) and hash out the price.
This does mean that you can't hide any plot points in their shopping adventure, but it can be a small price to pay for the time you win back.
Best Answer
Any spell that can boost armor will work.
There's no real problem with casting barkskin or mage armor prior to transforming; the spell effect will carry over after you transform. Polymorph doesn't block any ongoing spell effects. While your statistics get replaced by the creature's, spell effects aren't your statistics, they're the effects of a magic spell and consequently carry over to your new form.
This is explicitly covered in the Sage Advice Compendium:
So the easiest thing is probably mage armor (or in your case, the armor of shadows invocation), which should get your Giant Ape form up to AC 15, which is nearly your target. I don't know of a good way to get barkskin with the group you're with, but I think there's an easier answer on your own invocation list.
Alternatively, another player could cast mage armor on you -- it used to be "self only" in prior editions, but these days it can be delivered by touch. You may need to be a little thoughtful about how your gear is set up, though -- if you were wearing armor in your human form and then polymorphed into an ape, your ape form would be a valid target for mage armor but the spell would end as soon as you reverted because you'd then be wearing physical armor, which breaks the spell.