How Can I Manage My Visa Status While Renewing My UK Passport in Thailand?

Hi guys, could anyone please advise on this scenario:

Current 30 day stamp to expire on March 26th, will extend 30 days until April 26th. UK passport expires Dec' '20 - any long term visa I get will expire with the passport (I am told, so I want to renew it before I get a longer term visa + it's very nearly full, only 1 or 2 full pages left). If I can get the passport renewed within the next 30 day extension period, will the last stamp go from old passport to new? If it takes longer than 30 days, what would happen, I'd be overstaying? I doubt very much it would take MUCH less than 30 days, I am sure I will be cutting it very fine and probably have to do another visa run pretty much immediately after receiving new passport. UK passport cannot insert extra pages unfortunately. Thanks for any tips!