The surface area of your entire 75g tank and everything in it plus the 1500 filter is your current bio filter.
You are going to be loosing a good portion of your current bio filtration when you move just one part of the bio filter (the 1500 filter) to the new 200g tank. I would expect a mini-cycle to happen when you make the move to the new tank.
Hello; This! I agree completely. The beneficial bacteria (bb) do not know that we expect them to be only on the dedicated bio-media we place inside a filter. My take is they colonize any solid surface in the tank. Probably more colonies where there is some water flow.
That said the ammonia spike should be fairly brief especially if you do a few things. I would move the entire filter from the 75 gallon for a few weeks that way you get the greater number of bb to help seed the tank. The bb are slow reproducers compared to lots of other bacteria so it will take a few days to get a new balance.
Another thing is to reduce feeding or no feeding at all for a couple of days. That way there is less metabolic byproducts during the first days. I would likely do light feeding with two fasting days each week for about a month.
You can do more often water changes (WC) for a time.
Get a fine mesh bag or some panty hose and suspend bags of the old substrate for a few days.