Yes they are correct you will have to leave and re-enter the country to begin your METV, why not do that instead of extending your visa exempt entry? Also the 60 day visa exempt entry you mentioned at the end of your post has not yet been finalised yet or out into place 1st June was a speculation but nothing yet.
There is no work around, you have to leave the country and either repeat the visa on arrival again or if you are able to apply for the tourist visa that will give you 60 days at an embassy or consulate in a neighbouring country
Basically before your last day of entry the visa allows you in Thailand, the re entry permit doesn’t pause your visa it jus keeps it ‘live’ so you can enter on it. For example, you leave with 45 days left, return 40 days later you’ll get stamped back in for the 5 days you have remaining on that visa
If I understand your message you are applying for an evisa whilst outside of your home country which is something you can’t do and will likely result in the application being rejected.
If applying whilst outside/not departing from your home country you have to apply in person at an embassy/consulate. Best to check with the individual embassy as some you have to book an appointment but typically takes2-3 days to process from experience.
As you arrived on visa exempt entry you are indeed allowed ONE extension that will be for 30 days and cost 1900 baht a passport photo and a few documents.This can be done within 30 days of your stamp running out but some immigration offices will send you away and tell you to come back when you have around 7 days remaining, the 30 days get added to the end of your visa so you don’t lose days for doing it early etc.
After this extension if you wish to stay longer you would then have to leave and re enter the country.
So it’s 30 day extension not 90 days. The official rule is only two border runs by land in a calendar year. By air there is no official limit but after a few you will be told by immigration no more and you’ll have to get a proper visa for your length of stay. They are cracking down heavily since Covid on people living in Thailand and multiple visa exempts/tourist visas.
As for the how long do I have to stay outside of Thailand for it will vary at every border and every immigration officer some will happily stamp you out and back in in the same hour other will refuse and tell you to come back atleast 24hrs.
There’s a good chance they will flat out reject the application as you can’t apply for a visa whilst having a “valid” visa.
I’d email them there’s a chance maybe they can cancel your current visa and you can reapply that way maybe, however you will have to pay and go through the process again.
Unfortunately it’s your responsibility to make sure you fly within the 3 months of validity sending them an itinerary would not change dates or post date an application.
If you are leaving and re-entering Thailand on the same tourist visa like you said
1. Be sure to get e re-entry permit or the visa is dead the second you leave the country.
2. You maybe aware but if you leave after say 20 days of your 60 day visa an re enter you don’t get 40 days from entry you get what ever is left on the stamp you originally had. It just keeps your visa alive it doesn’t pause it.
To answer Your other question the 2 entries by land border is for visa exempt and your visa entries will not count towards this 🙂