I’d say maybe a combination of your two plans….do some fixed wing private pilot style flying while you’re finishing up active duty and then get on with the first regional you can. My thinking is that it’s been awhile since you’ve flown fixed wing so that would ease the transition to FW a bit (i.e. make regional training smoother) without delaying building 121 time that will get you to a major. Not so sure that spending the time and the money getting a CFI is worth it.
Not a previous helo guy but had a couple of friends that were in similar situations….
I’d also consider getting some interview prep now. I used Emerald Coast Interview consulting and would definitely recommend them. You don’t need this prep right now for your regional interview – but, at least with Emerald coast, you pay once and then can use their services indefinitely. So you can discuss your current situation now and then use them again when you come up for your major interview. Coming right out of the military, I also just learned a lot of basic airline life stuff from their seminar.
Best of luck, congrats on retirement!!