Are these burnouts to begin with? Or are they pieces cut from 3/4 x 12 flat? I ask because, as far as I know, there's no such thing as 1018 or 1045 plate.
In the hot rolled annealled state there's little difference in physical properties of 1018 and 1045. 1045 won't mill as well as 1018. For what you've described, it seems like Blanchard ground A36 plate would be a good starting point. From what I've seen over the last few years, the quality and consistency of plate is far better than that of HR low carbon flats, which are going to be stocked as A36, and not 1018, by most warehouses.
Another option, if they want a little more strength, would be burnouts from A572 Grade 50 plate. (50ksi min yield vs 36ksi for A36) Its decent to machine (as plate goes) and has always seemed somewhat more consistent than A36 when I've had occasion to make parts from it. I priced that material in 1/2" plate earlier this week from Ryerson, and it was 15 cents/lb more than A36. Given that your blanks would weigh about 60# each, the $9 or so premium over A36 would be worthwhile IMO.
If they insist on a medium carbon material, I think its Ryerson that has a material called Freemax 45 that's good to machine. Not sure if its resulfurized or some other process to help machinability, but it cuts pretty nice. Been 20+ years since I bought any of it though, so I don't remember any prices relative to A36. Doesn't stick in my mind as being particularly expensive though, and the difference between it and plain old 1040 or 1045 flat would be worth several bucks on a part with a lot of machining. The same thing is likely sold under other names, but Freemax is the one I remember.