IIRC, I had my saline trial using a loaner pump from the clinic a few weeks before starting on insulin. I was then on vacation for a couple of weeks, and when I came back I started on my brand new "out of the box" pump using insulin. If you haven't already, perhaps it is worth asking the hospital to do your saline trial earlier on a loaner pump (their current timeframes might be because they are looking to do the trial on your actual new pump)?
The other option you might want to discuss with the clinic is going onto insulin between appointments (e.g. start on saline Tuesday, start on insulin Friday). I can't see why you would need to go back to the clinic to start on insulin - the training should be the same; they would just need to give you the insulin vial as well as the saline vial.
Failing that, it does sound like starting on the pump and then going back to MDI for your first trip might be a good option. When you start on the pump, you tend to want to minimise variables while you get your basal rate sorted out, and travelling to another time zone can be a big variable.
If you do go ahead with travelling on the pump straight away, I'd recommend doing a basal test or two before you travel. Also, you might want to check that the clinic will give you enough supplies for your trip - I tend to take extras when I travel, and if you are new to pumping you might find you need more while you're getting used to e.g. set changes. It may be prudent to take both pump and MDI supplies with you, so you have those as a backup in the (very unlikely
) event you have issues and need to go back to MDI.
On adjusting time zone on your pump, I've tended to switch to destination time zone (and meal timings) as soon as I get on the plane in the UK for trips of more than a day or two.