'69 Barracuda T56 swap, floor, cross member

it'd be quicker to slip in some 1/2" plywood spacers just to check viability than remove the heater unit and mod' the tunnel some more. if you gain the clearance you need just swap in steel spacers and you're done. also you mention the headers will hang lower, that's not the case. the motor is still bolted to the k member the same, all you've done is raise the body by 1/2" up from the k. so in relation to any of the suspension that's close to the ground the headers remain the same.
neil.

You’re putting the headers lower to the ground with respect to the body of the car.

Whether you consider that raising the body or lowering the headers is up to you. I think it’s safe to say most of us set the ride height of the car based on the height of the body and not just the K frame, so, I’d say the headers would be getting closer to the ground because I’d be keeping the body at the same height.