Is the boat new or used?
Only if the tank is full to oveflowing--and I'm sure it was by the end of the week (more on that later) can waste in it flow back toward the toilet...the level in the tank would have to be at least as high as the inlet fitting from the toilet 'cuz waste can't jump up into it from below it. However, unless the tank vent is blocked, it's far more likely to overflow out the vent than it is to back up toward the toilet. If the vent is blocked, pressurizing the tank, waste displaced by new was is gonna go wherever it can...and that's back toward the toilet--sometimes explosively.If the backflow were holding tank contents, the water wouldn't just be blue (the use of blue chemicals in the tank is another subject we need to discuss), it would also be dirty. Same would be true if it's only backflow of waste left in the head discharge line unless the hoses are new. If it's clean, I'd look for one of the chemical inline devices in the head intake line. If you don't find one, Jim Rushing's guess is a good one, especially if the head discharge hose runs uphill from the toilet for any distance--waste/flush water left is flowing back downhill.I don't think ANYbody knows what a joker valve actually does. It's only supposed to prevent a flood...it's not supposed to prevent slow seepage...in fact, any joker valve that's had more than a dozen flushes go through it can't prevent seepage. If anything is getting back into the bowl via the head discharge line, replacing the joker valve is not the solution...the solution is: figure out WHY there's anything in the head the discharge line TO flow back into the toilet and eliminate that problem. Replacing the joker valve to stop backflow is tantamount to just putting a plug in a dripping faucet to stop the drip. The only difference is, you'd have to replace the joker valve about once a month for the "plug" to be effective. Check the level in the tank to make sure it was actually emptied when you pumped out...if the vent is blocked, it'll still be mostly full. Check both your head intake and discharge plumbing for uphill runs from the toilet...whatever is left in either hose will run downhill into the toilet. How old is the toilet? What make/model? If not new, when (if ever) was the last time it was rebuilt? Are there any vented loops in the system (do you know what a vented loop is?)?Now...about holding tank capacity: You didn't say how many gallons it's rated to hold, but it's not a bottomless pit. The average adult uses the toilet 5x/day. You used the marina facilities for the "important stuff," but each of you still used the toilet at least 3x a day. Flush water averages about a half-gallon a flush (more if you've never learned how to conserve by using the dry setting)...so including waste, each person is likely to put an average of 1.5-2 gals a day into the tank. That's AT LEAST 3-4 gallons a day for 2 people...more flush water means even more. Divide your tank capacity by that amount to find out how many days it takes to fill up your holding tank. If your tank is 20 gallons or less, and you spent at least 5 days aboard, you prob'ly started overflowing it late on the 3rd or 4th day. If you don't know where your holding tank vent thru-hull is, you can prob'ly find it if you look for a blue stain on your hull.