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The ETA GMT movement is very widely used. It’s in the Farer GMTs, the Bell & Ross, etc.
It’s thin and reliable but the quick-set jumping hour functionality is on the GMT hand (like the original GMT-Master), not the local hour hand (like the GMT-Master II). People on the internet seem to get in a tizz about that.
The Tudor GMT movement has the “superior” jumping local hour hand, but they have also had a lot of issues with the date not changing properly on them. They had to take a lot of them back to be fixed (which has probably made the supply issues even worse). So I wouldn’t expect a BB58 GMT for a good while, if it ever happens.
Actually I could see them making a second (third?) generation BB before that, with the same basic dimensions as the current one, just thinner.
According to this the ETA 2893-2 which has GMT hand and date is 4.1mm thick
https://www.eta.ch/en/our-products/mechanical-movements/mecaline-specialities/eta-mecaline-specialities-2893-2