Welcome to the forum!
Unfortunately I don't have a lot of advice to give - I moved to the UK with two suitcases and my cats, which is probably not the ideal situation for most.

I used PetRelocation.com to move my furbabies and would swear by them time and time again. It is very expensive, however, so I would definitely not recommend using a relocation company to move your dogs if you're trying to keep your costs down as the whole process really can be DIY.
Sorry I'm not of more use. Again, welcome to UKY and good luck!