as the orders are currently written they are supposed to only stamp you in for the period of insurance. This should be noted on the new visas by the embassy. However, if you are outside the period of insurance noted they are supposed to ask for proof or make you insurance buy from an approved Thai company.
To answer the second question, the requirements are on the UK website where they describe the O-A requirements. However, I don't remember if they took down the sample form in the last few months.
You can find it elsewhere but you don't need to have that form filled in. Just words that are equivalent to what is on the website.
You can email or call the London embassy if you are unsure but I suggest that your send your doctor what you need and see what he or she saud first (unless time is a factor).
Will your future wife be going to live with you right after the wedding? If so you may not have to do anything depending on how many times you plan to visit Thailand over the next few years.
Otherwise the METV as suggested by Steve Mathers is a good option.
The other option, once married, could be to get a Non-O multiple entry visa based on marriage from an embassy in a country in the region while it is still possible, e.g. Savannakhet. Some embassies may require less documentation than others.
It could see you through as much as 15-17 months depending on how you use it.
If she is unable to do this then she needs to contact the airline and if they say it's okay, cross her fingers that she gets the same answer when checking in.
I'm starting to think he didn't overstay 27 days but he was here 27 days after his initial visa expired i.e he entered about 2 months after a TV was issued.