I've finally found a way to use this gelli plate that approaches the fluency I desired. Contrary to the 'roll and pull' demos all over the internet, I had to discover for myself that the way to create what I wanted to was to wait until each layer dried on the plate before building up the next one, as well as to wait a good long time for the paint to set against the paper so that all the layers come off the plate. Therein lies the secret. Most demos suggest thin paint. For me, a nice thick layer works better.
I am loving the power of this discovery!