I hate to break it to the OP, but an FO losing an UG is probably not losing it to another FO, BIS or not. Sure it might happen, but with loads so high these days and very long UG lists ( >40 very common) it is much likely that you are losing your UG to higher elites.

This week as a DM on a Q fare I was 2 of 40 with 0 seats available for an MD during mid-day, off peak. I checked all flights that day and other flights had a max. of 1 open F seat on the seat map which may not have been a truly available F seat. And there were no weather events or delays forcing IROPS, just oversold planes with 1/3 of the plane being elite. RDU-ATL.

Folks who make FO on one MR or by Amex spend are not sitting on many planes so I wouldn't lament other non-BIS elites keeping you in coach. Might happen, but chances are very low.