How can I manage my visa situation in Thailand with a tourist visa and extensions?

Most of the options given in comments should get you close to your end date but please beware that entry to Thailand is never a guarantee if it appears as you are trying to stay long term without correct visa in the eyes of the IO on day of entry than don't be surprised if you are questioned they don't need a reason not to like you and deny entry Chokh di

Do not ASSUME that its going to work good. Just an opinion.

Correct

Suggest extending for 30 days at immigration then after that go to Vientiane and apply for another 60 days

All should be ok

Then after that extend for another 30 at immigration

Then go Vientiane and return to Thailand and receive 30 days visa exempt

That should get you to may

So if you arrived 16 October and get your 30 day extension, you should be okay until the middle of the month in January.

You can then do a border bounce (DO NOT GO TO POIPET) and get a new 30 day stamp. It might be better if you find an agency that will take you there and make sure you get out and in with no problems. You can apply for a 30 day extension to this visa exempt entry.

If you did it right at the end of your previous stamp, you should be good until around middle of the month March.

You can do one more land border bounce for visa exempt (you are limited to 2 per calendar year) and I would definitely recommend using an agency, and once again staying away from Poipet).

Again you can apply for a 30 day extension and if you did it right at the end of the previous stamp you should now be good until middle of the month May and you are ready to go home.

If you go to the embassy and get a tourist visa, you're still going to have to exit the country and re-enter again since you'll only get 90 days from that visa and you need about 120.