To me combat is always the most tedious/draggy part of a PbP, no matter what system or who's running. I think it's just impossible to escape given the format.
I just thought of something. In the previous game I was in, the DM would give us the AC/HP of the creatures we would face so we could directly rp our own hit, misses and kills. Mini-bosses, bosses or outstanding creatures, however, had their stats hidden.
Would that be good for us?
There were other things he did, but they weren't that much of a help. I guess one of the useful ones was the bundling of enemies initiative together, rolling as a group or pairs rather than individuals, which helped in making combat a little less drawn out.