Okay, done!
Firstly, I had to wipe all existing replays (well, I didn't
have to, but it was tidier this way). This shouldn't be a huge deal to anyone but myself, as no one else had submitted any replays yet.
Anyway, the need to fill out data such as lemmings saved etc manually is no longer an issue - it can get these from the replay file itself! However, you do need to record your replays with the newest version of Lemmix (or NeoLemmix). If you already made a replay with an older version, you can simply load it then re-save it with the new version; you don't have to execute the solution again.
For Lemmix and NeoLemmix replays, it will now also show the time taken to complete the level.
There isn't any skill-counting yet, sorry. I still need to add that.
So yeah. This should be a tad more convenient now. Please do give it a go, so you can let me know if there's any issues. It doesn't seem anyone else had used it yet - a few people had logged on, but no one had submitted anything - so if it continues to not see any use, I'll probably take it down - no sense in having it there and taking up hosting space, or working on it in general, if it isn't being used.
EDIT: Just to add, on each level (if it has any replays), it now displays the highest number of lemmings saved, and best time achieved. If more than one replay are tied, it will list the one that was uploaded first. It currently doesn't distinguish between different mechanics sets when doing this, though.