Control Strymon pedals with 5-pin MIDI and TRS at the same time (trying to circumvent the QC's midi limitations)

I have a Disaster Area DMC-3 that controls my Timeline and BigSky. I also want to be able to send midi clock from my QC to the Timeline, but if I did that, I would then need to run the DMC-3 through the QC and then into the Strymons (the DMC doesn’t have MIDI-in). However, since the QC’s midi capabilities are limited, I cannot run MIDI-through and MIDI-clock at the same time…

Does anyone know if I can run 5-PIN midi-in and TRS midi-in to a Strymon pedal at the same time? Ideally, I’d send the DMC midi via TRS, and the QC midi via 5-PIN (or vice-versa).

Admittedly, this may be more of a Stryom question, but it only came up because of the QC’s limited midi functionality, so I figured maybe someone here has experienced something similar.