Re: Like a hot melt glue gun stood on end
>> interesting aerodynamic problems. <<
Possibly not too many, the aerodynamic impact will lessen rapidly with altitude and thrust gimballing will become more important. CoG will stay somewhere in the middle between the converging motor & payload.
Having the fuel sufficiently stiff to survive launch stresses does sounds like a new rocket problem though.
For small rockets no payload separation system may be needed, the spent motor can just ride along until the whole thing drops out of orbit.