I'd try a blow-dryer, rather than a heat gun.
A heat gun may shrink it TOO much.
A combination of popping them with a pin, shrinking them slightly, and pressing them down, is probably your best bet.
Just be careful not to "tent" them.
That's when the vinyl sticks to itself in a wrinkle.
Those are pretty much impossible to remove, without cutting them out, and stretching the vinyl to cover the gap.