Hi,
I would. I would try pushing that nap closer to 12.30pm (capped at 2hours). Re: BT, I wonder if you've got into an UT/OT loop and hence the BT shenanigans - that is UT for nap and consequently OT for BT which is not helping the EW. If it were me, I would move the nap to 12.30pm (we usually move in 15min increments) and do BT at 7pm.
HTH x