Don't worry about it. Take pictures with the film and developer you have.
Honestly, there is ALWAYS something better than what you have. Once you have the "perfect" film and developer, why bother taking any shots until you have the "perfect" camera and lenses?
Just use what you've got. The difference between Tri-X and TMAX400 at 1600 is subjective, not objective. The difference between developers is meaningless until you know how to use at least one.
If you haven't heard "good things" about HC-110, it's not because it's bad - it's been used for ages for a reason, with legions of quiet fans. Raving about HC-110 would be like raving about water - it just works and is very versatile 🙂 You will see zero benefit from Microphen if you haven't used anything else. What is "better" for one person is simply better for them. I've never, ever heard someone criticize a photograph because of the developer used. Or even the film.
TMAX400 pushes nicely, but it has a different "look" than Tri-X. You don't need Neopan 1600 to shoot at 1600 or 3200 EI. It's worth learning how to use TMAX at those speeds, especially if you want to use a faster film. You lose range but are often shooting in contrasty lighting, so you get a better sense of how to capture what you want in a scene. This, in my experience, improves your exposure with any film - you get much better at identifying differences in lighting and how those differences get translated onto film.
I shoot Tri-X right now, but some of my favorite low-light pushed shots are on TMAX400. I think Tri-X might have more usable range when pushed to 1600 or more, but it's not a big difference, and certainly not one I would consider a deal-breaker.
FWIW, Kodak suggests 7.5 mins. in HC-110 (dil. B) for TMAX400 shot at 1600. I'd start there. I think you'll be pleasantly surprised.