Agreed for the EVA Air check-in part. Also, likely nobody will ask for this at the airport. However, the dates mentioned by the OP are 92 nights / 93 days. That will get him into trouble either way. So, something needs to be done.
As for the field on the online check-in of EVA Air: I am pretty sure that the field asking for your visa number is optional. Just leave it blank and likely nobody will bother you upon arrival at the airport. But just in case, be prepared to book a journey out of Thailand on the spot then, if they do.
If you really want to go down this road, forget about illegal constructs of nominees and companies. What you could do is boy the land in her name. Then lease the land back for 30 days from her in your name (maximum amount of time legally guaranteed), then build a house on it in your name. Depending on how old you are - that should be good enough.
You are correct, that "Brits" get stamped in for 60 days (59 nights) without a visa upon arrival. But you have your terminology wrong: you don't get a visa on arrival. What you get is not a visa at all, but a visa exemption (or visa waiver if you wish).
That visa exemption can be extended once in Thailand one time for another 30 days - giving you a total of 90 days / 89 nights in Thailand. Day of arrival counts in Thailand, hence the difference between permitted days / nights.
So, your booked dates won't work, as the distance between your mentioned dates is 92 days. You would need an actual visa to legally stay for that period. However, there is no ordinary tourist visa good for 92 days (expect for the DTV, which would allow for 180 days stay / each entry). There are common TR tourist visa good for 60 days (59 nights) that can also be extended another 30 days in country. So, TR tourist visa and your planned visa exemption entry are currently no difference with regards to permitted days.
While Thai immigration rarely checks for return flights, your operating airline is well within their rights to ask for proof of a return flight within your allowed days of stay - as they would be the ones responsible to transport you home in case of denial of entry. Strictly speaking, that would be 60 days - though most airlines would be okay with a return flight within 60+30 days = 90 days / 89 nights. I personally have never been bothered by any airlines (including great EVA air) with this, even though I usually fly one way without any return flight whatsoever. Still, the airline is within their rights.
Not sure what the best advice would be now. Maybe someone else with experience from the UK could chime in. The Royal Thai Embassy in London is one of the fastest in the world to issue visa, though I doubt they would be that fast.
Maybe you would need to change your return flight date. As mentioned in another response, getting a cheap throw-away flight out of Thailand within the initial 60 days would also do the trick - you would still be overstaying for 2 days. Maybe best to actually leave Thailand for a few days to a neighboring country midway in between if you don't intend to change your intercontinental flights.
Yeah. They kind of didn't think that one through, as usual. ED Plus to allow people to stay for finding a job, but then no clear process on converting that visa. In theory, it is possible to get a B / working visa in country off of any current stamp - if the tons of required documents are provided. A little easier if aiming to work for a school / university compared to a private company. Brandon gave you the detailed outline.
Note sure this is the best one ... but to give you an idea / example of something people are using. For residents in Germany there are better alternatives. I would assume for the UK, too.
There used to be a service offered by the agency behind this group greasing the wheel for (guaranteed) entry even with a difficult travel history. Wasn't cheap. Don't recall the details ... but others here might. I believe it was this service: