Yeah, it would be good if they allowed that. I know of some teachers who have been told they should be able to get their non-B visa from Laos next month, but so far no indication of whether that will happen.
There are thousands who need to border bounce to get a new entry or who need a new B or O visa. It's not been possible to do this and won't be until the borders reopen. I haven't seen any indication that those affected will be denied this option and will be forced to go back to their home country, but maybe that will happen. We should know soon as a decision re the amnesty will need to be made in the next few weeks.
Can't say I'm optimistic, although Laos has had 0 cases for a while, but as my family are stuck in Laos, I'm hopeful. But in respect to the OP's question, if the border remains closed, the amnesty will be extended.
Do you want to go back to the UK, or just get a new visa/entry? Either way, we should know soon if the amnesty will be extended. If the borders with Laos and other nearby countries open, you can hop across and get a new visa/entry. If flights start again, you should be able to re-book to go back to the UK as FinnAir have only cancelled as all flights from/to Thailand are still restricted.
If you want a work permit do you have an employer that is able to get you one? If so, when the borders re-open get the paperwork from your prospective employer and get a non-B visa from a Consulate. Otherwise it looks like an Ed visa for studying or another tourist visa, which may be declined as you're not a tourist. A final option is Thai Elite if you can afford it.
If you're in Bangkok you have plenty of choice. My boy is at a city centre international school (British curriculum) and it's affordable. PM me if you want the details.
We'll know for sure by the end of the month. It will take at least a month (July) for everyone to leave and flights will need to start booking by 1 July. Another extension is certainly possible.