Another welcome here.
A pellet pit will do a better job of seasoning cast iron than a gasser or any other direct flame cooker. The reason is indirect heating. You run the risk of burning the seasoning going the direct route... I have
seasoned several pieces of cast iron cookware in my pellet pit. If there was any sort of smoke infused into the seasoning, I sure as heck couldn't taste it.
350ยบ should be a good temp unless you are using an extremely low smoke point oil. Much better to season @ a lower temp longer rather than risking burning the seasoning. I would season no less than 1 Hr.
If the seasoning is tacky when you are done, either the oil layer was too thick, a common mistake, or seasoning time too short..
I like to let the cookware completely cool before removing it from the oven/pit.
The one drawback to using any outdoor pit is a rapid cooldown VS an indoor oven.
Let us know how it went!