I think your idea is very logical. Even one step better would be a flail mower to rent for the first go round as well so you know it works out like you envisioned but that might be a tougher find. It's not that hard to find a place to rent a compact tractor and it makes a lot of sense to know how everything will work out before committing much of anything.
When we bought our land last year I told my wife i'd be able to get everything done with an ATV and implements. The more research i did, the less I liked that idea. So I told her i'd just rent a tractor this year to figure out how things work and figure out what I really needed before diving in head first. Bonus season at work is in March and '22 was a doosie. So I made a liar out of myself.. But, I still think renting makes a lot of sense for lots of situations but the ability to have the equipment you want, when you want, without scheduling anything is real nice.
@Skeeter bought the Kunz rough cut mower I had planned to use initially going the ATV route. I doubt it mulches as consistent as a flail mower but it seemed like a pretty tough option that I'd assume spreads thatch pretty decent with 2 blades compared to a single blade