I don't mind you rolling dice at home; I likewise find using invisible castle more trouble than it is worth (since one can easily just keep rolling on it until they get the result they want). I can appreciate your desire to speed up the process when you post. My own responses can easily take me half an hour to over an hour to compose if they're involved and complicated. Frankly, with four young kids at home to take care of I can't imagine how you also find the time to run two PBP games with so many players in each. My hats off to you for pulling it off; it's a testament to your skill in both fields.
I also don't mind you rolling on our behalf, it's just that without being able to see the process we're kind of left to guess what, if anything, was rolled that then lead to the results you describe.
I'm not certain that I'd agree with you when you say that I'm viewing the combat through a lens of how it affects my character. I did notice that many characters seemed to be able to cross the large crowded taproom with surprising speed. It's just that it's generally easier to address the issues that affect my character directly than it is to point out the issues that happen to benefit other people's characters. Other PCs might resent someone butting in to point out a detrimental rule-clarification IYKWIM.
I agree with you when you say that it's largely a matter of gaining the players' trust. This being our first combat together I am keeping a critical eye out for anything out of the ordinary. Please understand that seeing some PCs moving curiously faster than I'd expect while also seeing NPCs performing seemingly impossible combat manoeuvres tends to raise some red flags in my mind. Obviously players have to give the DM some leeway to describe combat in an exciting way. And certainly some people prefer a fast and loose style of play, but I'm afraid I'm not really one of them. I'll admit it; I prefer sticking closer to the rules so that I can know what to expect in combat and plan accordingly. I enjoy the tactical side of combat. I'll also admit that when I first see a DM's preferred style of play I get worried about rule-calls that seem a little arbitrary.
I'll admit that I'm likely being over-critical but it's largely due to the fact that you invited us to offer our comments and point out possible mistakes to you. Sorry if it's becoming bothersome for you. Either way, I'm not letting any objections I have slow down the game; Maelicent just keeps going with the flow of the combat as described whether I agree with what's happening or not.
For instance, dropping and then re-rolling initiative seems rather confusing to me. Maelicent didn't intend to pause in his attack; there's always been a threatening creature worthy of his arrows in the tap-room since the combat started. Now I'm wondering if he lost the opportunity to move and fire or not during the interim. Also, he's inexplicably dropped from first to fifth place in the initiative order. To me at least, this seems like the same combat that we started with, especially since one of our opponents was still in fighting shape and planning to flee. Maybe you could ask us if we're done taking actions before you drop initiative next time. :\