Unfortunately, swapping tanks, especially large tanks is never an easy operation. I've done it a few times and it's a job that needs to be done properly so don't take any short cuts. I think your biggest problem is saving the bacteria in your existing filtration system. To help with the cycling on the Newtown, you really need all those bacteria alive and kicking. Is there any way you can get a very large reciprocal that you could fill with existing tank water and keep the filtration running on it until the big tank is full and ready for the filter? a lot of people keep what we call water butts here in the UK. Basically they are large barrels, normally made out of plastic that are used to collect rainwater. One of these would hold enough water for you to run your filter on until the big tank is completely full.
Because you want to put the big tank where the smaller tank is, you are going to have to dismantle the whole lot so I would definitely think about using something to keep your filtration running. I wouldn't worry about anything else, keep as much water from the 75 gallon as possible. However, it's not going to be a disaster if you can't, just make sure you use a water condition now before starting up the filter again on the new tank. In fact, I would probably advise you to put some stress zyme in. Failing that, prime or stability will do the job just as well