Congrats on the new kid!
I tried something a little different this year at camp. I spread seed, then used my weighted tire drag in one direction. Then went the oppostie direction. Theory is to flip that dead stuff over to get the seed in lower. Seemed to work good. PRobably used 80lbs/acre of rye and 8-10 lbs /acre of clover seed. Seemed to work pretty good.
Your probably ok this time of year, but working an air cooled motor hard in low speed is torture on the motor. Pick up an electric fan up front. Looks like a recon. I had a 2004 and a 2020. Lubricants need a certain velocity to make an oil wedge. Working an ATV diff hard in low speeds is rough on that too. Consider annual oil changes. it's ok to use regular car diff oil of the same weight. Those diff's take like 3-10oz of oil. Cheap insurance.
No till is considered light tillage up to 30% soil disruption in the AG world. That mower and tractor up?Could spray, wait a few days, spread seed them mow low, then roll.
Turning up the soil will help seed contact for sure. That i a good bit of thatch. I haven't had good luck with that much thatch. Turning us soil will wake up a bunch of old seeds. I'd be tempted to say yes to a single pass of that 12ft disc. You can try this experiemnt without tillage, but if you don't get good results, turn to doing that in the fall. Definitely give it 2 sprays. Definietly spray 2-3 week of good warm weather after tilling it. IF you spray in the spring, the soil may not be warm enough to get warm season stuff to be out and germination. Running that roller after tillage might be too much for that honda 250 too.
I did not play too much with the recons in that regard. I also have a 420cc liquid cooled 4x4 rancher. I have the same roller, although mine is dented up pretty good from heavy clay with rocks in it.
Controlled burn would be awesome. Never did one myself. NY isn't a fun state in that regard.