2HOT Thermometer “in flight above 7,300 meters” at Minmus

Should I even bother with trying a low energy transfer, utilizing Mun to get to Minmus?

No. Minimus has an eccentric orbit. Attempting to gain a gravity assist from the Mun that will provide the exact normal/antinormal force to end up in a good Minmus encounter at the exact right point of it's orbit will require some very exact calculations.

The most efficient way I know of is to match the orbital inclination before making the injection burn. From a parking orbit of approximately 100km this just happens to be as it rises over Kerbin.

I remember having this problem with older versions of KSP (around .16 or so?). Are you using the latest versions of KSP and mechjeb?

If both are up-to-date, I'd try installing KSP to a new directory (keep the original if you'd like). Reinstall mechjeb and try again. I've had a few cases where this has fixed odd issues.