Our approach is almost identical. lol. It costs us space, but runtime is O(n)

You're right....also using a switch statement as you did saves us space, instead of storing vowels in a data structure. Although the space used for the small amount of data we are storing is essentially negligiable.

This is very bothersome to read. Clearly it works, however, readibility of this is an issue.

concatenating Strings with += is really expensive and should be avoided. Also, we reinvented the wheel here with your "reverse" function. Consider using StringBuilder().

Fails for Capital vowels

QUESTION : IS SB.TOSTRING() ANY FASTER THAN NEW STRING(SB) ?

This is hard to read.