Sorry, not wishing to sound overtly negative or disrespectful. Merely highlighting the fact that there are different bikes for different activities and that there is a very good reason for this. I did think you were joking, but I apologise for being flippant.
Spending a lot of money on adapting a design that is already highly compromised for use on road is, in my opinion, a waste of time and money. If you have space, spend what you would have spent on the Brompton and get a mountain bike. I have a freeride MTB, XC MTB and a hybrid for commuting. I used to think one bike for all uses was sufficient and ended up with extra bikes because I kept getting it wrong. I now have three rebuilt machines that are very good bikes (not the latest and greatest). Each is suited to their respective areas of use. I have thought about a quirky bike project just to be different, but this would be an excess beyond excess.
Getting a bike with geometry to suit your physique and intended use will make a massive difference to your ride! Brompton's, by comparison to a large wheeled bike are about as far away from a tailored experience as one can get. Please try out some other bikes to see what I am getting at (if you haven't already).
It doesn't have to cost the earth to acquire a new machine if you are able to pick up an old bike/frame online. All the bits you could need are available online (www.ebay.co.uk, http://www.wiggle.co.uk, http://www.chainreactioncycles.com). Frames can be bead blasted and powder coated for as little as £35 if repainting is required. There are also cheap bikes in most stores, which would be the simplest and easiest route. I try and support my local independant bike shop, but I find they mostly cater for entry level stuff. The ones that don't are great. If you have one such shop locally, give them a shout. They should help you whatever your needs and wants.
Good luck in whatever route you take!