It's funny though because TWEWY can work on the R4DS (orginal flashcard) but the almighty CycloDS can't.
The only flash card that has a problem running TWEWY is the M3 (and possibly some of the obscure cards including the DS-X).
For the rest of the cards (Cyclo, R4, Acekard), the performance of TWEWY is determined by your MicroSD. It's a very picky so unless you have the famous Kingston 2GB Japan MicroSD, you'll likely experience problems.
And yes, closing the DS lid might help you pass the problematic part, but the best way is to download a save right after that part. I believe the rest of the game plays fine.