No question that it would be a hassle to swap wheels, but for someone who wanted to store a trailer in a garage with a door it won't fit under it's at least an option, especially if the purpose was extended winter storage and the trailer wasn't going to be moved for several months.
Probably the easiest way to install the small wheels would be to fabricate a pair of simple wedge ramps out of two or three stacked 2x6's with beveled ends, jack up each side in turn with a low profile floor jack (Harbor Freight sells a 1.5 ton capacity "aluminum racing jack" for $99 that's low enough), put on the small wheels, slide the ramps under the wheels & drop the wheels down on to the ramps, then roll it down onto the ground and into the garage.
Haven't had any reason to check the bolt pattern on our 2307C, but based on aftermarket trailer wheel listings it appears most trailer hubs have the same 5 on 4.5" bolt circle as most mid 50's through mid 70's Ford, AMC and Chrysler passenger cars. Trailer brake drums are fairly small, so it shouldn't be difficult to find a pair of bare steel wheels that would fit, and most of the rim portion of the wheel would be cut away to get the diameter down.
Probably not worth the trouble, but if a rubber contact surface was desired on the cut down wheels, it should be possible to cut most of the sidewalls off small utility trailer tires and stretch the tread section over the cut down steel wheels.
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2307C / 2002 GMC Sierra 1500 ext cab (BellTech lowering kit, AirLift load-lifter air bags on rear axle, on-board compressor)
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