I think the cloth room did a good job considering what you asked it to do.

Solution: In MD try to 'sew' a smooth support patch on the inside and let that take care of the 'structural behavior' of the area during the simulation in the cloth room. The decorative front part would be a 'soft decoration' in the cloth room. Define as different materials in MD to facilitate grouping.

Also in real clothing using a back patch this is not an uncommon solution to maintain complex folds while the cloth is under stress. Sew folds to the patch as necessary. The patch can be made invisible.