I have a Stephens 200 in 223 that i had problems single feeding a round. it annoyed me at first, but after 2 or 3 range trips, I figured out exactly how to manuever the round and I can get it in there almost always first try without issue. It's basically second nature now. It's definitely a personal preference thing, but it might save you a little cash if you give it a little more time and try to get used to it. I was also thinking about the conversion you mentioned as your other option, but I have no experience with it.
In regards to the fouling, if its consistent that's the most important thing. Again, a personel preference thing, but I would recommend finding a good cleaning routine that won't be soo thorough that it causes the POI to change. After all, if it's dirty enough just a few shots later (maybe more??) that it's back to the normal POI, I'm not sure you gain anything by ever getting it that clean. As a benchrest shooter you may disagree, but IMO the purpose of cleaning is to maintain accuracy. If cleaning/specific cleaning hurts accuracy, I wouldn't be doing it.
The Jeep has been a lot of fun, but time to come back to my first hobby.. shooting.