transport co. reccomendations for '64 Dart

I guess this really isn't the appropriate forum except that it relates to a '64 Dart. But if the deal goes down and it is shipped back, any auto transport companies recommended? I know they aren't all the same, and some have lowball initial quotes and then all these hidden charges later, etc. This would be for (relatively speaking) short haul from lower NY state to DC area of Maryland.

Are there any scams or traps to watch out for?

I did put in an online request to one company, but it turned out to be a site that sends it to a bunch of companies! Nine quotes have rolled in, ranging from 550 to 800, but still want to know who MoPar guys are using. Will also see what I can find online about choosing a carrier.

Thanks,
Bob B