I would count that aqua-tech filter out in being much use for helping cycle a new tank unless it's got separate sponge that you never replace, only squeeze out. On bio wheel filters, the bio wheels themselves are intended to be the biological part as far as I know.
As TwoTankAmin suggests, if your 55 has been up and running for some time (months/years), has original substrate and hardscape, is not overstocked and is a reasonably maintained tank, you should be able the pull a filter or both filters without the cycle crashing. Like said, everything else in the tank should contain adequate beneficial bacteria to keep things going for you. If your tank is heavily overstocked or undermaintained, count any/all of that out though.
I just started up a brand-new 55gal tank by using ~90% of the substrate, hardscape, plants and filtration out of a 29g I took down and gave away. All the 29 had in terms of stock was a bunch of endlers/guppies and assassin snails. They all went in the 55g too along with my new weather loaches.
It's like running with scissors I know, but I haven't even checked water parameters in the new 55 yet. I've done this tank swap over enough times now I may be getting over confident.
Your goldfish situation.. Do you intend to keep common/comets or fancies? As you know, the common or comet variety in nature grow massive. Like said, you can make it work for awhile in a 29g, even with commons, but it's far from ideal. Fancies would be a better choice, but again, 1-2 of them is the bigger problem here IMO. You don't have the ideal space for more than a pair and at that number they're likely to be skittish and stressed.
There was a time I kept two carnival won comets and two fancies in a 55gal. They all started growing to be beautiful, especially the carnival fish of all things. They were fun and I kept nitrates not to exceed ~20ppm w/ one fin-level water change per week, but that tank eventually sprung a bottom seal leak and lost ~25g of water all over my living space. In a panic move, I re-homed the goldfish to a family member's massive, secluded (and awesome) pond. Never saw them again.. Not sure if that's good or not. LOL.