Follow-up:
We just returned from a fabulous trip, where I ended up retaining the EuropCar rental. With the full insurance (piece of mind) and the "Europe Package" (though we did not use any of the elements - GB sticker, head light deflectors, etc.) what had appeared to be a reasonable cost (160 GB pounds at the time of internet reservation) for 5 days bludgeoned to a hefty 400 big ones.
All said and done, I don't think (have not done any comparable analysis to back this up) I could have done better (moneywise) for me and two of my kids (16 and 12) with the rail travel, with as many spots that we visited - Gatwick-Dover/Calais-Brussels-Antwerp-Amsterdam-Brugge-Calais/Dover-Gatwick with the car resting in parking lot when in the cities. The added flexibility of bending our schedule at whim was a plus too.
We had some wonderful discoveries on the road - the memorable one being a great gourmet experience at a rest stop while crossing from Belgium to Netherlands (near Breda, if my memory serves right) at the restaurant named La Place - wonderful food and great ambience, unexpected for a fueling stop. The driving in Brussels was unusually aggressive.
Lessons Learnt:
1) GPS is the greatest things since the sliced bread ;-)
2) You can't see/do as many things as you plan on the paper.
3) Everything costs more - and takes longer - than you think.
4) There are never as many minutes available on the cell phone Sim cards as claimed/advertised.
5) It always helps to frame your expectations through advance readings and video watching (Rick Steves, Smart Travels/Rudy Maxa, Passport to Europe/Samantha Brown - all are wonderful resources easily available through the public libraries to borrow).
All said and done, it was a great trip and was the tip of the proverbial iceberg of numerous future Europe trips.
As a bonus, we discovered this forum which we will continue to tap into, for our future excursions abroad. Thanks everybody, for your help!
-Mehul