The way I look at it is this:
People have busy lives. I work full time and take night classes in the evenings for example, and I know others do even more than that. Strict initiative is generally bad, as if Player A has time to post Monday but can't because he has to wait for Player B to post, but player B can't post until Tuesday, it screws everyone up.
Simply splitting it into rounds where everyone takes their turn, then we begin the cycle again fixes that to a degree. In situations where you don't have time to post for a couple days and people are waiting, simply PMing myself can work in a pinch, as I can roll your character's actions into a post and cover the die rolls. It unfortunately means you lose out on the opportunity to describe the event from your character's perspective, but it keeps things rolling.
I think it would be best to keep the RP more towards streamlined gameplay. Sure you could find a reason to roll dice for practically everything in a tabletop RPG, but this format makes it a bit cumbersome. Viewing it as a normal forum RP with some dice tossed in rather than a traditional tabletop RPG jammed into a forum format is probably the best way to go.
If in your post, for your "turn" you shoot at something or attempt picking a lock, or do something that is not a guaranteed outcome, include a roll at the bottom of your post (or multiple, if you're doing something like shooting and include the damage roll). If you aren't sure if you need to roll or what you need to roll, feel free to PM me or ask me in the OOC. You can PM me your roll ahead of time and I can tell you the outcome so you can include that in your post as well to make things easier.
Apologies for the text-wall.
Also,
@Nohbdy still with us my dude?