I would do as suggested try to get as much old filter media into you’re new one . If I was in this position I would dose the whole tank volume with prime for a week to cover your fish and to give your new filter a chance to catch up again to your stocking levels. I would dose prime once every 24 hours for a week incase you get any ammonia and nitrite spikes. Other people may disagree with me but if it was my tank Thant’s what I would do .
I can see why you thinking along these lines, the logic is there.
However, dosing Seachem Prime every 24 hours will amount to basically overdosing the water column.
What happens when you add prime is this binds ammonia, ammonium, nitrite etc but also prime will deplete the water column of oxygen, usually just temporarily. But in overdosing prime, in extreme cases, this might effect your water parameters and possibly even harm your livestock.
And also what you have to remember as well is that livestock will ingest whatever you add to the water column so this may have detrimental effects on their bodies, therefore we kind of always say the less of you adding any chemicals to the tank, the better.
Caution is always advised whenever one adds chemicals or dechlorinters, read the label and research or ask first before doing these things.
Edit - swapping over the old filter media to the new filter is fine, just put in everything from old filter, sponge, biomedia and ceramics etc to new filter.
Plus don't forget there will already be loads of bb in the substrate, tank glass, plants and decor etc, so the effects of a new filter with established media will be minimal, possible minicycle but this is usually sorted by the bb colonising the new filter casing and the numbers will rise to the desired equilibrium to maintain water parameters fairly quickly, normally two or three days.
So do keep an eye on your ammonia and nitrite readings over the next few days and anytime you see 0.5ppm or over, just simply do a large water change with dechlorinated water.
