I think a decent fix to begin could be to just have the screens/levels be shorter in the first world. Like if there's a room where you have to do 2 kinda hard jumps, I'd just cut it up in two rooms. I didn't mind that the jumps were hard, I'd have already had a better experience just by not having to repeat a segment before an hard jump.
For the pit/spikes where you have to superjump out from I think you could probably widen it a little bit, just to leave the player more wiggle room to maneuver around and making the pit slightly shorter to accomodate for the change in length.