Personally I don't see bristle worms as a problem, they are a free part of the CUC. I have them all over my entire system and have never given me an issue. Their population is controlled by the amount of available food source, whatever the source in the tank may be. Again my personal view.
If you want to dip then have at it! I'm not gonna tell you not to do it. Just be aware those bristle worms are also in your substrate. You can clear them of the rocks but if you don't take care of the ones in the substrate all your work will be for nothing. I've never dipped my rocks but I've had to store them a few times going through the multiple tank size upgrades. Also when I moved from one house to another.
Since the rock is already well cycled. I would try to fit all the rock into the available space in your other tanks after your dip before you go out have spend money on something. That way you don't have additional costs of having to get an air pump with air stone and heater (if you don't already have them). If you run out of room in the tanks I've put mine in one of the 20g round blue hard plastic bins from Lowes they are cheap in comparison to brute containers. Throw in some water from the tank you are cleaning, an air stone and heater and call it good until they go back into their original tank.
For your corals definitely put them under the light of your other running tanks. I've done that just put them in another established tank on the substrate not touching and never had an issue. Just acclimate them if the levels are different.
