You can go pretty big on a 15" rim. Something to the order of a 37" tire.
With gearing the wording is kinda funky by increasing your gear ratio I'm assuming you want go down numerically? E.G. a 3.73 set to a 3.07 ? On a truck easiest way is to upsize your tires. You are running a 30x10.5x15 tire right now. If you can fit it, might want to consider a 32x9.5x15 is you could find one. That would numerically decrease your gear ratio and also cut down on your rubber width.