I have a couple of suggestions for random endgames with no clear win for one side. I think such endgames are also useful for training. I have a few collections. I think you can make good use of these collections in an endgame training tool.
One collection has 157846 endgame positions, which came from Stockfish test suits (
github.com/official-stockfish/books - the file endgames.epd.zip). In fact I am running round robin tournaments between 16 of the top 25 or so engines using these positions, without tablebases. In my matches, cutechess-gui selects a random position and the engines play a game pair from that position. The games are quite interesting to watch.
Another collection that I obtained from
github.com/jhorthos/lczero-training/wiki/Opening-Books has been used in Lc0 testing. Here you will find 14 piece endgames (1M+ positions) and 16 piece endgames (1.34M positions) (in fact there are games leading to these positions). I believe the positions have been extracted from caissbase. Each position is evaluated by an Lc0 net, and given a q-score. Positions with q-score in the range -0.25 to +0.25 are quite balanced (roughly -+ 30 centipawn on Stockfish scale) and they get more imbalanced as the absolute value of the q-score increases.
Finally, a large collection of mate in N puzzles is included with Scid vs PC. I am not sure if the collection is from the epd position database here
http://www.nk-qy.info/40h/. If not, you have yet another collection.