I doubt that will work, if the pot is filled enough for you to drag a board over it you will get all the dross on the top in your joints and solder all over the board.
What your talking about is a selective solder machine.
This has a solder bath but with an approx 8mm nozzle where solder comes up higher to solder the area around a PTH pin.
Unfortunately these cost some 30 times what you are prepared to pay. Perhaps you can look for something smaller and cheaper
Youtube will likely have videos of the process.
Or how about just using paste dabbed onto whre you want it and reflow the whole thing in a toaster oven?
Try looking at auctions and 2nd hand gear resellers.
EDIT: Now I have seen the board itself (would not load before) a simple wave soldering machine would do this board. same advice as above.