Hey - just checked out your tank photo. Nice!
Yes transferring rocks and sand will help - especially the substrate (sand) as the large surface area on the particles mean lots of room for bacteria.
Seeding from a filter shouldn't be too hard either. The carbon - especially if its been in there a while - should have plenty of bacteria on it. If you can get the carbon granules out just put some into a small net bag (you can improvise with cut-off stocking) or even loose in the bottom of your air filter.
If its not loose, make a net / stocking bag with some sand or gravel in it, put it in your existing 55g tank's biowheel filter for 3-5 days at least, and then transfer it over into the other filter to seed it. Or, even simpler, just make a bag with some of the established tank's sand substrate. (I'd do both, but maybe I'm overly careful).
Not as perfect as fully cycling a tank, but a MASSIVE improvement on nothing at all!!
Just as an aside people get carbon mainly for absorbing chemical impurities in aquaria, which is what it is sold for. In fact it is only effective at doing this for its first week or so in any tank. After that what it becomes is a great additional site for bacteria filtration - acting a lot like the ceramic noodles that one also sees around the place - but next to useless as a chemical filter.