From personal experience, I have raised my Testosterone consumption during periods I know it was dropping due to reasons like the above. However, I am already on a baseline of TRT, so I don't really receive any negatives from doing this.

For you:

Would taking a form of TRT benefit you during the time period that your Testosterone drops and improve your performance back to normal levels? Very likely.

Would such a treatment be encouraged? There have been times people have gotten on TRT just to lose weight, then come off with a bit of PCT. They were happy enough, but it is typically not encouraged if you don't want to deal with a few side effects.

When your body gains any amount of Testosterone from an outside source, it will inevitably produce less on it's own. It varies from person to person, but some suppression will take place. So first, you want to make sure the amount that you use will provide the benefit you want and account for the loss of a certain amount of natural Testosterone production. When coming off TRT, that suppression remains for some time. For your case, that would make the recovery of T slower after but the performance during better.

Outside of actual Testosterone, there is also things like Clomid (side effects) & HCG (expensive, and primes you more than anything) which will raise your natural production. Potentially Enclomiphene may be a better short term boost with less side effects/suppression than typical TRT, but it's a bit less well known. Our partners in peptides, Triumph Health listed above, could probably have a consultation with you about that specific use case as they're more comfortable with it at the moment.

Sorry for the long reply, TL;DR:

You can, it will work, there will be side effects, it would probably be better to just be on TRT (not trying to promote here, just true opinion). If you're low enough during these crashes to need a boost you're probably sitting pretty close to low normally.