So, in the department of "It feels wrong so legally it must be correct" (a handy guideline for Bar Exam questions):
UA really should be willing to move the ticket around in line with how they'd handle a paid ticket misconnect. However, given SQ's touchy relationship with the rest of *A (e.g. their effective refusal to release premium cabin space to partners) I can see them being less-than-willing on that front. I agree that OP should contact UA.
That being said, has OP looked at changing the IAH-ORD leg instead of ORD-MUC? Domestic space might be easier to come by (even if you end up having to do something stupid in terms of connecting).