I worked on my starter today as well, installing new wiring.
The motor is out so i have plenty space to play around, what i did notice was there is some "play" on the bolt and stud that hold down the starter on mine. (440 source mini starter 123-1000)
After seeing that it made me wonder as i remember your issue, i don't know what starter you are using but in the previous picture your old starter also looks like the 440 source starter.
Could it be it shifted a bit after the first start which causes the starter pinion not to engage the ring gear?
I know it's a pain in the ***, but could be worth a try to loosen the fasteners a bit and see if there is play.
After pull outwards, away from the engine as far as it would go and retighten the bolts again to see if that helps.