Hi OP I've got a dc from a fresh cycle and trying FET soon using blastocysts too.
To transfer embryos you can either collect in an incubator from one clinic and drive them to the New clinic, or you can pay for a courier (the receiving clinic should be able to advise on this).
I wouldn't travel long distances for FET as there are scans etc which I'd find hard work, but it's a personal decision.
I think the success rates are similar for natural and medicated FET. To do natural you need to have regular cycles and ovulate each month, there is little flexibility in the tx as ET is booked for a few days after you ovulate/surge. I opted for medicated, as though it's slightly more expensive it gives a bit more flexibility for scan dates, ET etc as you can coast a bit on the drugs, obviously on natural there's no leeway as your body dictates when ET needs to be.
I opted to inject rather than sniff as you still down regulate on a medicated cycle. I found sniffing annoyed my nose and was three times per day, where injecting is just once. Injecting suprecur is much cheaper too, it cost me £17 for a ten day supply of injections, whereas sniffing would have cost £135!! Have a look at online pharmacies too if you want to get your drugs cheaper.
Good luck!