Non-mopar tech question, sorry...

It doesn't have to be the heater control valve. Don't zero in on that. It can be a vacuum malfunction anywhere and that's what it sounds like.

Vacuum is used in the HVAC box to "do" things. Operate blend doors and such. When you have a vacuum leak and accelerate, the vacuum goes away and "undoes" whatever it is that it's supposed to be "doing".

You have good vacuum at idle. Vacuum normally drops off on acceleration. Vehicles use vacuum canisters to help keep vacuum up to operate accessories like the HVAC system. When there's a leak, those accessories will fail on acceleration.

This is a very, very common problem with Fords along your year model. My 04 Ranger had the heater control valve rubber end rot off and do the exact same thing.

Once again, it does not have to be the heater control valve. It can be ANY vacuum hose or line under the hood or under the dash. The vacuum system is all connected so a leak will affect it all.