My weekday minyan is quite small so we tend to have regulars for each day of the week, unless someone has yahrzeit, is in sloshim or a visitor offered the amud.
That said I tend to daven for the amud on Tuesdays. This has only gone on since 2009 when my father Z”L was niftar. We have a family minhag that one doesn’t say even a reader’s kaddish while both parents are alive, I didn’t even daven for the amud on my Bar Mitzvah all those years ago.
For many years I lived in another CT city. The shul I belonged to was the result of a merger between Litvak (nusach Ashkenaz) and a Russian (Nusach Ari) shuls. The Litvak name went first but the shul davened Nusach Ari. I davened with my trusty old Tikun Meir Siddur–nusach Ashkenaz. For years the shammos tried to get me to daven for the amud and I always refused. He tried to sweeten the deal by saying I could daven my nusach. It never happened.
Now that middle daughter is to be wed soon and SIL will be in the neighborhood (working for me) I hope he’ll take over Tuesdays–he has a much better voice.