My T Hunter
You are correct. Provided you claim for your duty move and baggage journeys seperately there is no problem.
I have done so twice in the last 2 years without any hassle. If I remember correctly this claim is still done manually by PSF/HR. There is some paperwork to be signed up at the unit you are leaving then you take the completed paperwork and receipts to your new unit and the claim is actioned by them.
For the baggage move you can use your own car and claim petrol provided you keep the receipts. You can make as many journeys as you need up to the allowance. Alternatively you can claim the allowance to hire a van.