As Jamie pointed out, that in itself shouldn’t be the limiting factor. The E-350 shouldn’t weigh more than 12,500 pounds in the first place, or it’d be overloaded.
And since GCWR should be 18,500 pounds (should also be confirmed), that leaves at least 6,000 pounds for toad and motorcycle.
And if you believe Thor, the hitch should be good for up to 8,000 pounds. That too should be confirmed.
Unless there is something different about the motorhome in question, it should be OK as far as ratings are concerned. Obviously one of the first steps should be to weigh the motorhome and also the bike. If pickup is heavier than expected, it may be possible to take some weight out of MH by unloading unnecessary items in order to remain within GCWR.
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