If you're truly only hoisting to within a foot and a half of the masthead that's a pretty short hoist, so it would appear you do have the room to make that change. How simple it will be depends on how your gooseneck attachment is made. Riveted? Bolted? Welded? on a sliding track? Lots of potential variations.
Moving the sail up the rig will probably increase your heeling moment somewhat, but that should be manageable.
Another possibly simpler option might be to have the foot of the main recut to raise just the clew a 6 inches or a foot or so, lifting the boom enough to create some extra clearance.. Then the next time you buy a sail you could order a full luff length and get that area back.
Be careful, though, that a dodger 'tall enough' for what you think you need doesn't end up an unsightly block ruining the lines of the boat.. We have a very high bridge deck and agonized some time over the overall height - enough for access but not enough to look odd.. our relatively tight space for entry is going to keep us nimble - (that's our story...