I have moved several large layouts and found my best results are with a lot of volunteers around the edges. Worked great!
Those three wheel per leg furniture dollies come in a wide array of weight capacity which is reflected in their pricing.
The Harbor Freight dollies only are rated at 132 # each. Probably marginally OK if you never climb up on the platform, but I am getting the HD dollies today rated at 200 # (for another purpose but similar).