leave your tank the way it is. Cycling with uncured live rock is a good idea....FAR better than cycling with fish.
Cured or uncured doesn't really matter - there will be die off anyhow, when you're starting a tank, and you WANT that; that's what is going to start your nitrogen cycle.
If you really want to add another filter, go ahead - but it's not necesary at this point IMO.
Wait until your cycle is over to add the inverts. It'll take a couple weeks. Once the ammonia spikes, you'll even begin to see a little bit of life...pods and such. ...takes around 2 weeks to really see it.
Another suggestion....you can add a LOT of live rock NOW so u won't have to cure any later when the cycle is done (adding uncured LR to a POST CYCLED tank is dangerous b/c it might start a new mini cycle, which might lead the to death of whatever else is in the tank). If it were me, I'd stuff as much LR in there as possible to really get the cycle going.
That's a really pretty tank - keep us posted, and good luck! :joy: