Good to see a new post - and a new challenger for my crown. You are definitely on the right track but I think you need to think a little harder.
You can improve by knowing all the locations where keys can be found and then adjusting your route slightly to take advantage of that knowledge in the caverns. All that dropping and picking up could be better. Also, you're wrong about having to find a key before the Basement.
That's enough clues - wouldn't want you to get too good - I might just have to come back out of retirement!
Good luck.
P.S. If you want an easier challenge use the "view all" feature on the score board to see that I'm the fastest... but also the slowest. Beating the slowest time shouldn't be too hard - if you have the patience...
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Alright... I'm yet to get a great map for this route but I scored 2:14 on it today with a -terrible- run in the caverns:
From start: S, E. If you have the green key, open the door S then drop it and proceed as before, otherwise restart.
Continue picking up a piece of the main key, then down the the basement and take the yellow. Then S, E and jump down the trapdoor without dropping anything.
S, S, take main key, N, N and around back past the demon to the basement and straight up the stairs. Drop the parts of the main key, taking the green and keeping the yellow.
Head straight up to the attic, grab the handle for the main key. Drop down again, go through the barrel, grab the rest of the key and out.
This is different to the route you hinted at but is quite a bit better than my last, I'll see how fast I can get it with the right map.