I don't know if this is any help, but this is a spreadsheet I came up with on 9 May 2024 of BA codeshare opportunities LHR/LGW to BKK. Obviously this could well be out of date now.
It was made up by collating information from a variety of sources including GF and ExpertFlyer.
To book many of the options, you'll have to call up, and even then I don't know if they'll let you do it.
I too don't like short connections. Sometimes, the longer the better!
Edit my notes show I booked
BA123 LHR-DOH
BA6346 (QR836) DOH-BKK
BA2311 (QR839) BKK-DOH
BA7015 (QR15) DOH-LHR
...which worked well with the hotel's check in time, and gave me a couple of hours for the connection.