Before doing any type of major reconstructive surgery on your camper, I recommend you try two things first, one which has already been mentioned.
1) Empty your black tank, add about 10 gallon of water and a gallon of bleach. Go for a 15 minute drive then dump your tank. Rinse, and dump again.
2) With your toilet completely empty (turn your water pump off and press the peddle on the toilet), put a small amount of vegetable oil on the slide valve and slide it back and forth a few times to get it good and slippery. Work it a few times, then turn your water source back on again.
Although it may seem like the slide valve is shut, it's possible it's really not. They can stick open allowing smells from the tank to come up. The vegetable oil will not hurt the rubber seal, and it creates a lubricant, and act as a cleaner to soften any gunk that may be trapped in the rubber seal, where you cannot see it.
Chances are, the previous owner was one of those RVers who state they never had to clean their black tank. Well, now you know what happens when they don't get cleaned out every now and then.
A bit of bleach every now and then with a few gallons of water a couple times a year, going for a drive, and then dumping right away does a LOT to keep odors out of your tank. Once you get it clean out, simple water flushing will do it quite well also (after you get it clean out the first time). Then an occasional good dose of bleach and water will keep it that way.
Try it, before doing any surgery on your camper. You've got nothing to loose, and everything to gain. If this does not work, THEN consider one of the other suggestions listed above in previous posts.
I'm a believer in doing the least evasive, least costly attempts first, and eliminate simplicity before going complex.
FYI, run some bleach water down the Grey tank also. It won't hurt anything either.