I find that a normal SA axle (5 3/4") on a traditional hub like an AW, AM or even (if you like tinkering) FW fits a Brompton just fine. With non-Brompton-specific modern SA hubs like the SRF3, there can be rather a lot of excess axle sticking out of the left-hand side, but that's not an issue since the Brompton LH axle nut is open-ended (most traditional SA bikes have a closed-ended nut, unless they have a two-piece indicator spindle).
I think the big washer before the chain tensioner retaining nut is quite important for centring the tensioner as well as stopping the nut easting into the plastic, so I wouldn't leave it out.
What I think you need to do is to check the OLD spacing of your new hub vs the frame. Bromptons are very narrow, about 112mm, although they probably vary a little from bike to bike. The hub as shipped may be a little wide (they have no idea what bike it's going to end up fitted to) and therefore needs spacers removing, if there are any, from between the RH cone locknut and the cone. This entails resetting the hub internal clearance (done with the RH cone) and the bearing adjustment (done with the LH cone) afterwards, and you'll have to redish the wheel unless you removed the same amount from the LH side. It's all on Sheldon.
For the record, the spacing of a 5 3/4" axle SA hub can be varied from about 110mm up to 118mm (if you're careful, with pressed steel dropouts). The 6 1/4" ones are good for over 120mm. I have a stock of 1mm axle washers which are useful for fine tuning to match a particular frame.