I couldn't agree with this more. I am one of the folks that bought the TT bike while already having a road bike and I wish I would have done what you described below. Was I faster on the TT bike than on the road bike? Sure was! But I always find myself wishing I had a road bike fitted out the way the ITU triathletes have theirs set up. Stubby aero bars and all! The bike is just so versatile. Better for climbing, better for handling, and you can still get pretty darn aero.
Do I regret buying the TT bike? No, I don't not. Why? Because I really enjoy doing time trials. But it's just not as ideal for anything else.
I will make the investment in a high end roadie set up like the ITU triathlete at some point...but not now. I don't have the money after making the spend on the TT bike.
Start with a good bike fit. Once you have the coordinates (and have confirmed orthodoxy), work out if it is possible to get your current bike there. This can usually be done with some creativity (suitable selection of low-stack aero bars, stem, seatpost and saddle).
I would stick with the current bike if you can, a road bike is much more versatile than a TT. Maybe once you get to the longer races then a dedicated second bike will make sense.
Wheels can be added later, and can always transfer to a new bike. But they (and a different frame) are small fry compared to getting your body in a good position. If it's cost/benefit you're after, fit a rear wheel disc cover and just buy a deep front wheel.
Ironman Lake Placid - 2019
North East Regional Long Course Championship - 2019
Bucks County Marathon - 2019
American Zofingen Ultra Distance Duathlon - 2020