Lower-profile
tires can be used to keep overall tire diameter down while increasing wheel size, as long as load capacity is maintained (tough, since shorter sidewalls mean less load capacity, despite the larger wheel). Since ST (Special Trailer)
tires are generally only available in tall aspect ratios (75 and higher), and LT (light truck) tires are not available this small (in overall diameter), the choices are
commercial truck/van/trailer and
passenger car tires.
For small commercial tires in low profiles, I suggest checking out Continental's Vanco series, Michelin's Agilis, or Nokian's NRC 2; those are the ones I have found with possible sizes for my
Boler B1700 (a 17' trailer which uses larger tires than a typical 13' egg).
For passenger car tires, remember to de-rate the tire's load capacity by 10% for trailer service, and look for Extra Load (XL) tires to handle higher pressures and keep capacity up.
If increasing overall tire diameter significantly, remember that this will reduce the effectiveness of the
brakes, unless they are larger as well.