There might be another way to play Bb, Eb and E. Mute the 4th string with your thumb on those few chords. If you can wrap your thumb to slightly touch the 4th string and cause it the thud, you’ll at least be able to play the other notes. Also the notes on the 4th string are duplicates of the first. You just lose the re-entrant sound on those.
It might turn out to be tougher than actually learning to play a full chord, or it might be easier for you.
Also if you are having trouble changing chords fast enough to make the song flow smoothly, it is possible to change after the second to last beat, third on 4-4 time, and don’t strum on the next beat. Strum the new chord on 1.
Don’t know if any of this helps, but good luck.
John