[wingnut60]

A 20-ton jack is way overkill, and may be too tall to fit under the spring mounting plate.
Not sure what size mine is, but consider that you may have 20k gross, less the pin weight on the front jacks, leaving you with about 16k to lift / 4 wheels=about 4k wheel. Even a 10ton is overkill. Get one that will fit under for sure, and size it about 50% over.
As to the base--it will be pretty stable by itself on a flat concrete surface, so OK with that situation. However, if the surface is soft/dirt/gravel whatever, you will need a flat piece of something that won't bend/break/crack--and, then you have to think about the thickness of the support piece that causes the jack to sit higher and may not fit under the spring plate. If the surface is badly soft, the jack may just push the support/jack downward before lifting the wheel.
Always chock the opposite wheels, or have it hooked to the tow vehicle for safety.
The several trailers I have had and used bottle jacks--the biggest problem was always fitting it under the spring plate--placing it on the spring plate usually turned out very stable without thought to have some sort of cradle for it, which would also take away from the space in which to spot the jack.
Kodiaktrailer.com is the Kodiak website--they are located on the west loop I-820 in Fort Worth. 817-284-5141. Several threads/posts about needing to lube the caliper slides and torque the mounting bolts correctly.