Are you running bias or radials?
Another wrinkle in the mix for me was switching from a PUP with 12" wheels to one with 14" wheels. That was a major upgrade in construction, tread width and diameter, etc. You would probably see less of an improvement going from a 13" to a 14" wheel but it might be worth it.
Your 13" tire outer diameter is 24.1" and a 14" wheel and tire would be around 26.3" diameter. From the axle to your wheel well, you would loose right at an inch of clearance. If you have the room (or add an axle over/under conversion) you could do it. It would help with the typical Coleman/Fleetwood low clearance on their PUPs.