Hi Maria,
" Both plumbers snaked from a place in the basement near the floor drain where the water came"
Did they snake from a clean out in the house?
" The most recent guy used that video snake and found nothing."
Did he run the video camera all the way out to the street raiser and check the raiser? That's where we find most of the clogs in a line that runs from the house.
" Everywhere the snake went, the pipe was filled about 1/5 with water (which he stated was normal/good),"
Not in my book it isn't. You're talking about a pipe that has almost a quarter of it filled with standing water. The norm for standing water in a sewer line is a trickle of water that's not over 1/4". You're talking 4 times that much. Sewer pipes slope down one inch every four feet. This means they are draining all the time, EXCEPT when there's a partial blockage, ie

soft blockage).
"3 feet outside the house he found a 10 foot "belly". 10 feet in length, not depth, of a slight dip, but he said that shouldn't cause the prob."
I would be very concerned about the depth of that bell and what effect it has on the "rate of flow" of the sewage. If the flow slows down too much then solids will drop and began to build up into a clog.
" wouldn't the water come up at the drain closest to where everything exits the house?"
If the blockage's between the house and the street the first place you would see water is at the open clean out. If the clean out were capped the next place would be the lowest out let in the basement, usually a basement shower or a floor drain.
Your plumbers are missing a partial blockage big time.
" Both times, the water had receded by the time the plumber came, so no diagnosis was given."
I'm amazed that none of the plumbers cycled a washer or flushed enough water down the system to back it up. That way they could a least tell how far out the blockage was. I hate to say that the plumbers you hired were incompetent but they sure seem to be missing a whole bunch of the obvious.
I would call out a third plumbing company, tell them two other companys couldn't locate the problem and show them my post. Good luck and please keep me informed. Tom