It wouldn't be very efficient to do as you suggest and it will probably cause more problems in other areas of the house if you vent a portable hot air discharge into the return of your current system.

Air Conditioning operates by absorbing heat in a structure, adding additional heat to this absorbed heat via compression of the compressor and then to finally discharge it to the outdoors.

So if you discharge this hot air into the return of the existing AC, it will probably make the other areas of the home less cool, which would ultimately defeat the purpose.

I would go with what the AC company recommended with the proviso that it had better work! Sometimes, the problem with hot rooms is that there is no return air so the suply air cant get into the room. Ask them if a return would solve your problem before they install a second supply (and keep the first supply vent active, as simply moving it won't help a lot).

It hard to comment whether $600 is a fair cost to install a vent without knowing the level of difficulty. A portable AC is going to cost $300 - $400 and you still have to solve the exhaust problem. If your HVAC contractor is confident the second vent is going to work then spend the extra money and be comfortable.