I hate to cast doubt on your decision to buy a Brompton, but reading the first part of your post I thought the Bike Friday Tikit would meet your needs perfectly:
#1 It will go into shops better than a Brompton because it folds more quickly, it is lighter, and it rolls more easily (although the Brompton rolls you would never be able to roll it into any shop except a large supermarket because you either need to leave the handlebars sticking out or leave the seat up with the rear wheel susceptible to flopping out). Also you can't really use the Brompton rear rack for carrying stuff because the bike sits on top of it while folded. The Brompton does have a front bag that can be used, but as you said, the more you add the more you erode the Brompton's size advantage.
#2 It will travel just about as easily as a Brompton depending on your needs. In this regard the Brompton's advantage is that it can go into a standard suitcase with absolutely no disassembly when traveling long distance (just the standard fold) and has a better chance of fitting under the seat on local buses and trains. The tikit's advantage, however, is that there is a special suitcase designed for it that converts into a trailer (you only have to remove the seat, handlebars, and front wheel to pack it with plenty of room to spare), so you're not stuck with an empty suitcase at your destination, and since you can rest it on the ground while holding it it's better for crowded local transit where you might have to stand.
#3 The tikit would probably also be better for maintenance and repairs while traveling because it uses a derailleur, quick release wheels, and overall more standard parts. Plus bike friday has been known to send replacement parts overnight to far off countries (doubt you'd get that kind of service from Brompton).
#4 Bike Friday prides themselves on the quality of the ride. Personally I think the Brompton rides better than the tikit, but even the most reputable Brompton dealer in NYC says the main difference between the Tikit and the Brompton is that the tikit has a better ride and a bigger fold, so I guess I'm an oddball.

I hate to be a naysayer, but I don't think the Brompton is really designed for your needs. The Brompton is almost perfect for suburbanites commuting by rail, but in my opinion there are much better bikes for taking into shops or traveling.

Personally I decided against both bikes because the only bike I've found I can truly carry "quickly and easily and stealthily into the shop, with no difficulty carrying and no hassle from the staff that it might be too big" is the Pacific Cycles Carryme (made in Taiwan alongside the Birdy), but I'm not looking to travel or fall in love with cycling (just get around my city as quickly and with as little hassle as possible).

As far as the tikit goes, there is lots of info around the forum and internet. In particular here is a Dahon vs Brompton vs Tikit video showdown and a list of Bike Friday dealers in Taiwan.