In my experience, when I fly a new route, it takes about 3 times with the same crew in relatively short succession for them to remember me. Taking into consideration it won't be the same crew each time, I would put the number of RTs on a route at closer to 5-6 to see the same crew enough to remember me. The flights you listed are each 6-8K SM RT, which if you're flying multiple routes with that type of frequency, seems like you'd be a DM.

Secondly, there is no such thing as a BE UG on an intl route. There are, however, op ups where folks get 'upgraded' for various reasons, usually secondary to oversold in Y and so often higher level medallions will get bumped into BE. I've had probably an abnormally high percentage of op up success as I have documented elsewhere on this site but usually those are on tpac routes where I am returning to the US via HKG, NRT, or NGO. There are plenty of threads on FT about intl op ups.