I'm that single retiree you're referring to and I'm at~$3000 USD per month (and no girlfriend expenses), so I'd say you're about on target. $2000 budget would be a stretch in my view. Some will say you can live comfortably on half that, but just because you can doesn't mean you should. I came to Thailand to enjoy life, not to just get by.
Have you considered just waiting until November to come to Thailand? The 3 months will fly by. Certainly make use of an agent for both of you as it's the best way to optimize time (speaking from experience).
I understand where you're coming from as some agents are dodgy. Mine got me set up with a bank account where I then wired the necessary amount and I've been maintaining it with the proper balance for a couple years, and all completely under my name. So I think I'm in good shape.
Why glued to an agent forever? I can choose in subsequent years to use an agent or not. The stamp in my passport is the same regardless whether an agent was involved.
It's kinda nice two options are available to suit people's "best" approach! Good luck. Let's enjoy 🇹ðŸ‡. Some countries make it impossible to stay long term.