Well, I've answered my own question. After submitting the online contact form Saturday and again on Sunday with no response from them (weekend, I know, so cut them slack), I called and talked to a nice lady on Monday who said she would have their relocation specialist call me in around 10 minutes. Almost three hours later, the specialist called and apologized for his lateness as he'd had to deal with a pet-to-veterinarian emergency. Totally understandable. He confirmed they could handle my move and would either call or email me details about a Saturday morning virtual estimate later in the week (Skype, Facebook video chat, whichever program I wanted). Great!
Friday at 3:30 his time, had not heard from him, so I called. No answer. I left a message to call me back. No call back. Finally got a call from him Saturday at around 2:00pm his time, inquiring about whether I was ready for the call.
Um, no thanks. If I can't depend on him for the initial appointment/details, there's no way I'm going to risk depending on them moving day.
I had also filled out an online form the same weekend with Go Diego Go. They emailed and called back within a few hours, had me fill out an online form, and gave me their quote. They might be great, but without them having seen all my "stuff" I wonder how they could estimate the weight, size, etc. to come up with that quote...seems like there might be some surprises down the road that I'd prefer to avoid. I've read so many bad reviews about moving day surprises that I don't think that's the way to go.
On the upside, had success in scheduling a Friday appointment with the Beltmann Group of North American Van Lines. Their rep came to my house and walked around with his iPad, documenting everything I would be moving. Sat down with me to discuss, explain, and give me his quote. I don't think the "perfect move" exists, but I think this is as close as I'm going to get. I'll plan to add my review of North American - Beltmann Group once the move is complete. Hope it's positive!