Paul,
While 77gr Mk262 is no where near "standard issue", there are quite a few units who are able to get it issued to them.
MTN5FWD,
Several dozen (at least) of our members are using TA01s and TA31s on M4s with 77gr ammo, so this combo is definitely workable. The BDC "ladder" isn't going to be exactly on, but that's no big deal. Something somewhere has to be mechanically out of alignment if you're that far off.
Can you zero this rifle with a detachable carry handle? Do you need to be at the extreme ends of the adjustment range with front sight elevation to do so? If so, you could have a damaged upper with an upper-to-barrel misalignment. This isn't as uncommon as you'd imagine if your M4 has had a lot of weight mounted on the M4 RAS rails.
Next, check the scope-to-base mounting. Make sure the mounting rail on the scope is fitting correcly into the base. It doesn't take much of an angle change to make a big difference downrange, and if I were to bet, I'd say this is the most likely place for a misalignment.
Finally, the base-to-upper fit needs to be good and flat.
Please let us know how it goes, or if we can be of anymore help.
-Troy