Any electrician or electrical supply store is going to frown on the idea of using the dryer connection and plugs/cables to come up with that solution. Not that you can't do it, just that it won't be approved or up to code probably.

Most normal houses have 220v/240v by nature. The line coming from the pole is 240v, 2-phase so +120v and -120v plus neutral (ground). When it gets to the house, the normal 120v wiring is just one side of the 240v connection, plus neutral. Running 240v to an outlet is no harder than running a new 120 line, except you need 2 runs of 12/2 cable or whatever you use. By taking a connection off both sides of the box (e.g. where your power service comes into the house - the circuit breaker box), then using the 2 hots, you have 240v connection. Ground is as normal.

I am not an electrician but that's how 240v is hooked up, generally, from what I've read. YMMV. But doing that would be safer than adapting a system to plug into dryer outlet.

I have a CP-51 also but haven't hooked it up yet, but when I do, this (above) is the route I'll likely take.