Heads for a Magnum Stroker Engine

Markh, greeting! Welcome aboard!

Tell us a few things about the car now in order to not “Overkill” on suggestions.

What gear ratio is in what size rear end?
Tires currently in use?
Manual or automatic and if so, which one? (904 - 727)
The converter stalls at?
Weight of car?

Do you have the ATK short block now?
If so, does the block have a oil passage to send oil through the head?

Stroking a 318 to a 390 is a little more expensive than doing other stroker kits. Still, 390 is a pretty good move upwards in displacement.
Use a forged assembly for racing. It’s a little more expensive but it will be a more durable and stronger set up.
Are 360/5.9 engines hard to come by in England?