I do not agree with you: the Birdy could accept big chainwheel without the new chain tensionning arm around the chainwheel.

There are 9-32, 9-34 and 9-36 cassettes that fit on the 3gen Birdy but they require a SRAM XD ot XDR freewheel. Meaning that you need to change the rear wheel (or maybe find a Hubsmith XDR freewheel for the Birdy R11). If you do not need a longer gear, you can use a smaller chainwheel to have shorter gears (9-32 is 366% total range, 9-34 is 378 and 9-36 is 400%)
https://r2-bike.com/3T-Cassette-Bail...eed-9-32-teeth
https://r2-bike.com/LEONARDI-RACING-...ed-for-SRAM-XD
https://r2-bike.com/ETHIRTEEN-Casset...eed-9-34-teeth