I've been out of the country and returned with a TM30 filed in 2019 and I've asked Chiang Mai Immigration in person if I had to refile and they said no and I've never had any issues with it. Others have been told by CM Immigration that they don't need to either.
Per the other comments, a residency certificate is required. As for your International Driving Permit, you can only drive on it here for 90 days then you need to get a Thai license.
Unless you use a visa agent, there is no one place to organize visas. That said, not hard to do it yourself. Laos and Cambodia offer 30 day visa on arrival and Vietnam has a 90 day eVisa. You don't need a visa for Thailand unless you plan on staying in Thailand longer than 60 days at a time - 30 day visa exempt + a 30 day extension. Not sure how Cambodia and Laos work for longer stays - visas are probably available but you may not want to stay in either for more than a month.
domestically in the US? I have money paid into my Wise account in the US and then I transfer most of it to Thailand which shouldn't involved ACH or Wire transfers.
What does the top option say that you put the red line through? Wise or Wire? Side note, I haven't got any notice from them of changes and I'm currently waiting for my monthly pay to come in.