Some years ago I was able to do this at a station that had a similar situation with digital latency. Between the digital STL, digital processor at the transmitter site, and digital exciter, there was enough latency to make it pretty hard to use normal off-air monitoring. Fortunately at this station the aux transmitter was at the studio and the processor for that backup transmitter had solid multiband processing and an analog output. So a Broadcast Tools multi-relay box let me use the muting relay from the console to switch in this processed feed that sounded "right" in the headphones with no appreciable delay. When the mic was off, the regular off-air feed was in the path. Back in the transmitter room, the composite output of Mr. Aphex fed the analog exciter and it was all good.