There is two problems with that firebox, A) the grate does not extend across the entire bottom of the firebox and B)there is no shaker grate. I would suggest it is going to be very problematic.
Pices wrote: Because I am heating a plastic greenhouse, I am very concerned about ash and soot, not only for potential burns through the plastic but also accumulation on the plastic and blocking sunlight.
Anthracite would certainly be right up your alley as far as that goes.
I don't know if it is possible to build a coal fire that will last only 14 to 16 hours?
It's possible but isn't something you'll want to do, that's going to be a lot of work among other problems. If you need something that needs to be on demand your best bet is a stoker becsue that can reduce it's consumption to just enough to keep the fire lit.
One forum member here is from NC, he moved from NJ and took his EFM stoker boiler with him. He's in Warreton, not sure if that is close to your location. He'll be able to help you out some especially with a source for coal and the costs.