I don't know what the problem was in your case but every US / Canadian house has 120-0-120V supply so that high loads such as cookers and heaters can be sensibly operated. You don't get 3-phase in domestic installations there any more than we do here. So it's 240V, not 208V.
When I moved to Canada, obviously I took all of my UK workshop equipment and simply wired a multi-way extension lead into the consumer unit in exactly the same way as you would a tumble drier or cooker there. Everything worked fine, as you'd expect. Technically the motors spun about 20% faster (60Hz vs 50Hz) but that worked for me(!). The welders etc also didn't need any adjustment. Really nothing clever required and certainly no need to over think it.
You will find that any US / Canadian kitchen wired up in the last 15 years or so has so-called "split receptacles" whereby each of the twin outlets are actually connected to opposite phases, so in fact you can find 240V between the correct pair of wires. That's so you can run a kettle and toaster (for instance) simultaneously without tripping the 15A MCB. You can replace such a split receptacle with a US / Canadian 250V receptacle (different pin-out but same size plate) which will enable you to run a "proper" 3kW UK kettle – the US ones are feeble, being limited to 1.2kW. Then you don't lose the will to live, waiting for the damned thing to boil. When you next visit the UK, make certain to come back with a couple of 3kW kettles.
So have another go. You don't need the neutral connection – connect the motor L & N between the 2 opposite phases.
Murray