Thanks all for the guidance!

Yeah, I'm not very familiar with T2 (LHR used to be my weekly run on short haul but I mostly flew BA because of the Air Berlin (RIP) Oneworld partnership).
I also only realized that the LH lounge was closed after trying to find some lounge reports. I guess the reopened SQ and/or AC lounge would be nice to check out.

I think at this point, I'm leaning towards SQ/AC as I prefer my predictable 15min tunnel run (if my flight is not departing from T2B) over the unpredictable LHR security but I may try to check out the arrivals lounge if I land really early, there's no immigration lines, and the LH lounge is open (unlikely but who knows).