Don't think I can do much better than this, some minor mistakes in here but nothing major. My sum of best is 35:40, but there's some boss missplits in there so probably more like 35:55.

Other than new strats, here's the main improvements I can see:

Get the level 4 jump quicker. Don't go for safety cheeses, or go for them and get them quicker. Less careful play on last 3 puzzle levels.