I've rounded out my top cap bolt by using a bad allen key. I've tried most solutions to removing stripped bolts but none of these have solved this issue. If I use a large adjustable wrench and place it on the top cap and turn will this loosen the bolt enough that I can remove it? Also, I would prefer not to drill as I have a carbon fork and may risk damage if the drill slips in the removal process.
If it's an aluminum steerer with a star nut and conventional top cap and bolt, just use a big drill to go through the bolt head. This will remove the top cap. At that point you have various options. Presumably the bolt stub is corroded in place. You could try grasping it with needle nose vise grips, penetrating oil soak, etc. If it's corroded solid you could just pound it down and put a new star nut in for a quick fix. Otherwise, there are various ways of getting a star nut properly out.
If this is a plug, the line of attack is going to depend on the specific design. Most of them would make it pretty easy to drill out the preload wrench flats you've stripped sufficiently to get a wrench down into the plug expander bolt, letting you just remove the whole thing. If it's glued or the steerer has integral threads, you're going to need to get the threads moving somehow to save the fork.
Presuming we're talking about an aluminum top cap and/or bolt, I wouldn't be too worried about drilling. Go slow, use cutting fluid, and it should go smooth. You should have a pretty big buffer to the walls of the steerer.
The easiest method is to just drill out the bolt. If you aren't comfortable with that I would try the following. I would flip the bike over and remove the front tire. Obtain some penetrating oil (preferable a brand that includes an straw on the sprayer). Use a product that specifies use for rusty bolts rather than a generic lubricant. Spray the lube into the bottom of the steerer tube. An alternative method is tie a string to a small rag, soak the rag in the oil and push it in to the steerer leaving the string out for rag removal. Do this over several days. To remove the screw flip the bike right side up. Using SAE allen wrench see if one will fit tightly into the rounded hole, you might want to try tapping it in if its a close fit. If this proves try to epoxy an allen wrench into the rounded hole then turning it after the epoxy sets.