I can't help you with .308 as I have yet to acquire one, but I can offer some guidance on the .223/5.56 TAP.
First, their are a couple different types of TAP. FPD, TAP (red box), and then TAP T2. FPD and Red Box both use the 75gr BTHP bullets, with cannelure. I've never seen Hornady offer the 75gr with cannelure bullets, but it shouldn't be that big of a deal.
The FPD is offered in a 55gr and a 75gr. The 55gr variant uses the Amax bullet, while the 75gr is the BTHP.
The 55gr FPD chronos at 3250fps at the muzzle of a 24" barrel.
The 75gr FPD chronos at 2800fps also from the muzzle of a 24" barrel.
I don't have the numbers for the TAP red box. As for the T2 (which the bullet isn't available for reloaders) however you can substitute it for the regular 75gr BTHP.
The T2 chronos from a 16" barrel at 2750fps.
I also plan to replicate the TAP 75gr load, and just finished replicating the 70gr 5.56 GMX load.
I used CFE223 with standard CCI 400s, and was able to actually exceed the velocity within safe pressure.
I would suggest against the 55gr Amax to be honest. I have heard this bullet has a thicker jacket and doesn't fragment as well as other bullets. However, depending on your barrel length, and twist rate, you might be limited to lighter bullets.
Also look around at other bullets offered for hunting/defense. The Nosler bonded 64gr is new, and getting pretty good reviews.