An agent at the ION service center was eventually able to do this for me after consulting multiple times with a supervisor. He did not describe it as a "one-time exception" but it did seem like he was learning to do something he wasn't initially trained for. Unfortunately I don't think this is something that a non-PPS phone agent would be able to help with.

I think something in the system prevents agents from easily changing from an SQ-only award to an SQ-and-*A award, even if the charts are now identical and there is I/X inventory on all flights.

What I had
SIN-FRA on SQ booked in I class (Saver Award) on Day 1

What I could see on singaporeair.com
FRA-MUC on LH in I and X classes on multiple flights on Day 1 and Day 2

What the agent could initially see
FRA-MUC on LH in I and X classes but only on flights on Day 2 >24 hours after arrival, effectively forcing me to pay additional miles since it would just be considered an additional segment, not a connection.

What I eventually managed to ticket
SIN-FRA on SQ in I, connecting to FRA-MUC on LH in I.

Additional taxes and the fuel surcharge on the FRA-MUC segment was probably more than what the train would have cost though...