Re: Need for bottomless pit. Apparently fortifications carved into the natural bedrock at edges of the map serves as a handy infinite drain. Except where that's below sea level, where it might well be an infinite source of (salt) water. (NBT, NDT, NGTTs.)
Alternatively, apply advanced hydoengineering towards the end of creating "evaporation" beds. Tunnels/caverns which are designed to be filled with anywhere from 1/7th[1] to almost 2/7ths[2] of a water on average. You could even automate the process to empty your initial drainage reservoirs into the evaporation areas with pressure-plate controlled floodgates/similar.
Tune it correctly, with automated re-filling and shutting valves, and you could use the evporation of the water as a long-term trigger that (especially if you have seasonal weather helping you out, e.g. winter freezing that can predictably stall the process and stop it drifting over the years) can even floor/de-flood your entrance at just the right times for the caravans/etc.
Not easy, but doable.
(There's also the atom-smashing method. And the burning-lignite-in-container method. And others I have certainly forgotten.)
[1] Although while filling any large enough corridor/area of water with water, some leading 7ths will evaporate spontaneously anyway, so you don't have to design it to so close a tolerance.
[2] You could make it so that it's 2/7ths on average, minus a single 2nd 7th on one tile, and eventually that solitary 7th would evaporate, allowing another 2nd 7th into that 1st 7th slot, and exposing the original 2nds primary 7th so that there's two evaporations on the way (wherever the brownian motion of water-level takes the lower levels) ... And so on. But that would be slow at first. And probably a slower rate overall, even though you're dealing with nearly twice the quantity of water in one cycle.