Tommy,
I think you are still trying to push water up hill.
There is no such thing as a 'lightweight' conversion.
A Brommie with a motor and controller will weigh about 15kg.
Weight can be saved by a smaller battery, but 20 miles a day means you need 8-10ah, so that's another three or four kilios in a Brommie bag.
In your favour, you will only have to lug this on and off a train - twice - a day, which might not be too bad if access is good.
A few steps or other obstruction on the way will kill the job stone dead.
The only way I can think to save weight is to drive to the station, which will cut the bike journey to 10 miles a day, which in turn allows you to have a smaller and lighter battery.
Doing that answers another concern: 20 miles a day, even if broken up into five mile chunks, is a lot, day in, day out, even on an ebike.
As mentioned earlier, Brommies, good as they are, are not the most comfy of rides.
Having rained on your parade a little, we do have a member skilled in Brompton conversions - jerrysimon.
If anyone can build you a light e-Brommie, he can.
You could try sending him a private message if he doesn't pop up on thread.