I believe most local towing companies don't care what they flatbed its still $$$$$$ to them. I have seen heavy machinery on flatbeds and even a garden shed on one. As long as they have easy access to the item and can pull up close to it they should be able to do it for you.
Also, nice 1970 Camaro Z28 you have. I myself have a 1970 Chevelle SS396.
I may have someone that will bring it to me. This is a 700+ mile move. I also have a quote from a moving company. Both are reasonable for my boat-anchor VMC 340!
Back in the fall of 1970, I went down to Spence Chevrolet in Daytona Beach to look at a brand new 1970 Z28 they had for sale. I found it in the side lot; It was red with black stripes. Wow!
But right behind it was a 1970-71 Chevelle SS 454. It was white with black stripes and had a four speed. The very neat thing about it was it had a bench seat. I thought THAT would be better for dates than buckets!
My dad wouldn't co-sign for me so they never happened. A year later near Thanksgiving, I found the one I now own in the classifieds. It had headers and 14,000 miles on it. I paid $1900 for it.
To this day, I have never seen another Chevelle optioned like that one!