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I'd think 38 with 11-34 should do it right?
Biggest cassette possible, since you have to get a new derailleur anyway (105 R7000 GS, they can be found for less than asking price) with the 11 speed bar end shifter, I'd go for 11-40t* cassette.
*especially if your bike does not allow normal 11 speed cassette on the wheel, as the 11-34 and up required a spacer on a 11 speed freehubs body.
I'd like to have the option of dragging a 20kg mass up a South London hill without getting off the bike. I'd think 38 with 11-34 should do it right?