Whatever you're plan, I would have a plan B. Know which flight to KLA or PP you will take in case you're denied entry.
They have been cracking down, I guess. I *think* they're more concerned with people who come to Thailand and doing leave or don't leave enough. It sounds like you are here only part time. I think the Thai government appreciates those individuals who come to Thailand and spend money, then leave, then come back and spend more money.
Last time I came in, I came in on METV (,..Tourist Visa) and I got questioned. The supervising IO said with all the various visa options available now there is no reason to be doing back-to-back tourist visas.
I have been coming in on a long questionable visa history, it usually works out ok for me. I have gotten 'spoken to' a couple of times but they let me in.
Most recently, with a very legitimate visa, they gave me the hassle and this time I think they were serious.
They explained that with all the new visa options there really isn't any reason for doing all this silly visa nonsense.
If you "rescued" them, aren't they already rescued? You're job is done? Find the cats a home. What you can adopt-away, bring with you, I guess. There are plenty animals here to rescue, so you don't have to worry about that. I don't mean to be a dick but I suspect of your 13 cats, most wont really care if it's you that feeds them or so other American household. Hence, you're really just dragging the cats here, for your benefit not theirs.