Well I can't move fish until I'm sure the cycle has finished but I did take some of the pillow filler out of the filter sock in the 35G and move it to the HOB on this new tank. I'm guessing that what you mean by media. Also, the fake plants and scenery are from this tank which was an established tank when I picked it up today...until I broke it down and cleaned it. (used no chemicals...just sponge and water)
A good way to help your cycle is to squeeze the sponge/floss from your established filters into the new tank (or directly into the filter). Let all that gunk get in - lots of beneficial bacteria.
I was just thinking this new bowfront tank has some good ground floor space versus the 35 hex... would be good to get some of the bottom swimmers there into the new tank. If you're adding filter squeezings, you should be able to move fish fairly soon (so long as you do it slowly - a couple fish at a time).