Going to 16 inch wheels will allow you to get a taller tire. You will need to look at the 235/80/16, 235/85/16 or the 255/85/16
based on your existing tire size they are 28.3 inches in diameter
the 235/80/16 are 30.8 gain 1.25"
the 235/85/16 are 31.7 gain 1.7"
the 255/85/16 are 33.1 gain 2.4"
the height gain will be half the difference of the diameter difference
ie 30.8-28.3= 2.5/2=1.25 inch added height
you will need to check your axle spacing center of axle to center of axle and decide for yourself what is enough tire spacing between the tires. My trailer has 33 inch axle spacing so I could no way use the 255/85/16 tires as they would touch each other but the other two sizes would work.
You also want to check the clearance between the top of the tire and the underneath side of the trailer, take that measurement and for the sake of discussion lets say it is 6 inches now minus the increased height 6-1.25= 4.75 inches. If that is enough space for the trailer suspension to cycle without the tires hitting the underside of the trailer you are good. Trailer suspensions don't move too much only a few inches I believe but that will depend on the trailer and type of suspension used.