I think your uncured LR
will be enough to produce ammonia to start your cycling. So as long you dont have any livestocks in your main tank, its ok to cure the rock in there.
I've tried the Dead Shrimp cycle, it took me roughly 6 weeks have my tank fully cycled. The only minor problem i encountered is the smell of the decaying shrimp. Its not that super bad, its somewhat disturbing only.
Curing your live rock in your main tank, can make some mess i believe. Since some of the LR
coat will rot, to which will drop off to the sand. You can clean em by siphoning. I have no idea if the CUC's will clean it. I added my clean up crew 5 days after cycling to control some algae blooms. So far so good.
You need to be patient when cycling. Good luck!