Warning, I'm not directly answering your question about Tiny Windows. I have a newer HP "student" laptop that I bought (just after my newer standard HP when the last one died) for emergencies. Like warranty returns for a bad keyboard or touchpad which seem to happen a lot on laptops. The student HP is very SLOW with a processor and hard disk that are pathetic, even for a student model only one year old.

I started using the student HP with my Advanced Development Shell (ADS) for testing both in integrated and split modes. I wanted to see what older laptops might experience. It's horrible! I have no idea how previous versions of Access ever ran on these older computers, at least with a VBA intensive application. My testing showed the two biggest culprits were the processor and hard disk. No surprise there. I suspect removing the bloat from Windows is not going to magically make those two bottlenecks go away.

Second warning, I am also not answering your question.  I have no experience with Tiny Windows.  

In my experience, if an older pc has a mechanical hard drive and low RAM, replacing the drive with a solid state drive and increasing the ram usually gives a noticeable performance boost.  It won't be like a new pc but the increased RAM minimizes how often the pc uses swap space and the drive speed helps it when it does.  You might take a peek at Task Manager, Performance tab to see which component(s) are being overwhelmed when your laptop is "busy".

To follow up on Matt's response, I'm very heavy into VBA to give Access, with the ADS, a professional feel found in more robust products. Memory is often tied to processor speed, so it can be quite slow too, on an older or "student" laptop". However, even with everything in memory after the first pass of getting the db open and loading a form (insufferably slow), the subsequent slowness, in opening the same form again, tells me the processor is a big problem too. That said, I have a 12-year-old Toshiba laptop that outperforms the new student HP. Compared to older mini-computers, it's not too bad, but for today's expectations, I know users will balk. I can do lots of wonderful things with Access like colors and window layering, but all this comes with a heavy memory and processing price.

Going way back, my last mini-computer had 1mb of memory and a 20mhz processor that supported 10+ users hammering in hundreds of transactions a day as well as all my coding and administrative work. Even then, a form wouldn't take more than three seconds to load. We had a queue processor that would run updates after the nightly backup, and it would run for a good ten hours while everyone was comfortably sleeping at home.