Is there an easy way to check for the MMIC oscillating? Can I just look on a spectrum analyzer for any spurs up high in frequency?
If you have or have access to one with a wide freq range. A handy device to have is a "crystal detector" with some extended freq range, for example:
https://krytar.com/products/detectors/zero-bias-schottky-detectors/They turn up on eBay pretty cheap. Won't tell you what freq, just that you've got RF output and how much.
Keep a watch out for oscillation when playing with noise matching because MMICs are spec'd oscillation-free with 50-Ohm I/O. If the output is well terminated I expect it would be stable. Muck around with the MMIC alone on a test board, then transfer your creation to the transverter.
ALSO, with MMICs there's an important consideration; watch these videos: