I doubt if it's sewage...
Although you disconnected the intake hose, I'd bet you ran some sea water through the toilet, if only to test it. And I suspect there's a low spot in the intake hose in which sea water is still sitting and has stagnated to the point of putrification...when you flush, even though you're only adding water to the bowl with the shower head, the toilet still trying to pull in flush water...which is why you see a trickle coming from the rim. I think just flushing out the intake hose and channel in the rim of the bowl with clean fresh water and vinegar will solve your problem...Stick the intake hose in a bucket of clean fresh water to which you've added a quart of white vinegar and pump it through the toilet.But even clean fresh water will stagnate and eventually start to stink...so when it does again, you'll have to do this again. That is, unless you want to solve the sea water intake odor problem a much easier way:Go back to using sea water to flush...but tee your your head intake line into the head sink drain line (or vice versa, it doesn't matter which thru-hull, as long as the toilet and the head sink drain use the same one). At the end of each weekend aboard, close the thru-hull, fill the sink with clean fresh water, flush the toilet...because the thru-hull is closed, the toilet will pull the water out of the sink, rinsing all the sea water out of the whole system--the sink drain, the toilet intake, the toilet pump and rim of the bowl, and the head discharge hose.