Have you thought about visiting a nearby country for a few days? If you get the 60 day visa, then extension, that gives you 90 days in country. Then go visit Singapore or Malaysia, or anywhere for a few days, then come back to Thailand on exemption.
You SHOULD be fine to do that. Might get dodgy if you try more without actually moving around Thailand as well.
, I never said there is a restriction on being a tourist. There WILL be an issue if it appears you are trying to stay/live in a country (ie, not being a tourist). Thailand has rules, whether we like them or not.
Instead of doing border bounces, you might try to actually VISIT another country for a couple weeks. You are trying to live in Thailand on tourist entries. It would also help if you actually travelled around Thailand.
You are asking the wrong question. You cannot do anything on a tourist visa except be a tourist. You are needing to get the correct visa for the purpose of your visit. Whoever has given you your letter should be helping, or at least pointing you in the right direction.
I honestly would try and find a flight to Kuala Lumpur for a few days. I must say that leaving a border bounce to the last day is a recipe for disaster.
I was going to state that there are many varying types of deals the hotels will have with sites like booking etc. But I Think the bigger the chain, the better chance of getting a better deal directly from the hotel.