J.W.
My son was 3 years and 8 months before he started pooping in the potty. He had been peeing months before he finally pooped. I sent him to a mom's day out program 2x a week and he was supposed to be fully potty trained. He would show up in his pull-up, which they allowed, and he would pee in the potty but never poop. I just always prayed he didn't have to poop while he was there... so I can empathize with being on a timeline!
But once he pooped the first time in the potty, in his mind potty training was over. He was ready to use the potty all the time. I can count on one hand how many accidents we've had in 1+ year.
In my case, there was no gradual potty training, or no quick fix to get him to understand it sooner. I do think with other children it's more of a gradual process, whereas my son was "one and done." I felt some pressure because I noticed a lot of kids his age were fully trained, and I questioned if he would ever get it. He did obviously, but it was on his timeline, not mine as I would have prefered. We tried a lot of things -- bribes, pick out your own underwear, we even did a complete potty party to encourage the process and none of it worked until in his mind he was ready to do it.
After he pooped, we went to Chuck E Cheese to celebrate that very night. This was a carrot I held out for what felt like eternity and he still talks about his "pooping party" at Chuck E Cheese.
Good luck!
J.