2: A/Excellent, B/Very Good, C/Reject
1: A/Good, B/Very Good, C/Reject

Medians: A/Excellent, B/Very Good, C/Reject
A is elected

We can add a pair of opposite ballots to change this result.

2: A/Excellent, B/Very Good, C/Reject
1: A/Good, B/Very Good, C/Reject
1: A/Good, B/Excellent, C/Poor
1: A/Acceptable, B/Reject, C/Very Good

Medians: A/Good, B/Very Good, C/Reject
B is elected

Demonstrating that MJ fails the cancellation criterion is a bit more difficult since we must consider all possible cancelling ballots for A/Good, B/Excellent, C/Poor.

2: A/Excellent, B/Very Good, C/Reject
1: A/Good, B/Very Good, C/Reject
1: A/Good, B/Excellent, C/Poor
1: A/?, B/?, C/?

Medians: A/?, B/Very Good, C/Reject

Luckily it's possible to construct an election where B and C's medians are independent of the final ballot (as I did here), so we only need to consider the possible ratings for A. An Excellent rating will lead to A keeping their median rating of Excellent and winning, but no other rating will. A Very Good rating creates a tie between A and B which is broken in B's favor, and anything lower leads to B winning as well.

Now all that remains is to find another election in which A/Good, B/Excellent, C/Poor cannot possibly be cancelled out by a ballot with an Excellent rating for A.

2: A/Poor, B/Acceptable, C/Reject
1: A/Good, B/Acceptable, C/Reject

Medians: A/Poor, B/Acceptable, C/Reject
B is elected

2: A/Poor, B/Acceptable, C/Reject
1: A/Good, B/Acceptable, C/Reject
1: A/Good, B/Excellent, C/Poor
1: A/Excellent, B/?, C/?

Medians: A/Good, B/Acceptable, C/Reject
A is elected

So MJ fails both of these formalizations of Frohnmayer balance.