Correct - your seat assignment will be automatic if you book through raileurope.com. Through the other 'official' sites, you can select what type of seat you want, but don't get to choose a specific seat. IIRC, to change a seat, you need to do this on the phone or at an office, but I've never tried to do this.

It's very unusual for RailEurope.com to be cheaper, as it's effectively an agency. Have you definitely chosen the US site on eurostar.com? The UK site doesn't do discount one-way tickets.