What year is your 26 BHS? IS there a tab on the botto of the frame, near the bumper? IF so, you should be able to order the option factory rear cargo hitch. It is rated for up to 300lbs, though I couldn't confirm exactly at what distance the rating is for. We have carried 4 bikes (2 Specialized 26" full suspension, and 2 box store 20" full suspension without any issues on 2 or 3 trips last year. Our bike rack is a tray style, like a roof rack, that requires removal of the front wheel.
Or as Screwby posted, either (have someone) custom build one, or buy the one linked above that is a universal fit, frame mounted hitch. Just double check your bike rack to make sure it is ok to use on an rv. Only a few (maybe only 1 or 2???) rate their racks for rv use.
Just make sure you are not hanging to much weight out the rear of the trailer that you no longer have adequate tw!!! If you unload to much tw, you could have a serious sway issue.... Just use caution, and use the CAT Scales to verify you have the proper tw.
Good call on not using the spare tire rack. Chances are at some point it the rear bumper would end up failing. It isn't much different than the receiver hitch that bolts on just the bumper. Those usually fail at some point as well....