The DB site doesn't show timetables for city transit systems like the London Underground. The nearly two-hour route you saw was for taking various National Rail surface trains requiring multiple connections.
You should allow up to one hour to clear immigration/passport control.
If your flight is on time, you will be able to catch the 11:04 Eurostar to Brussels. If your flight is late enough that you miss that train, you should have no trouble catching the 12:57 Eurostar.
As I said in an earlier note, from Brussels you will have your choice of buying a passholder fare ticket on a high-speed Thalys train to Amsterdam or simply hoping on the next InterCity train (an hour slower, but "free" with your pass). Check the timetables on the DB site to see which train to Amsterdam will get you there the fastest. It's possible that you will have a shorter connection time if you take an IC train; but because Thalys trains are faster, you might arrive in Amsterdam just as soon--or sooner--by taking a Thalys train, even with a longer connection time in Brussels.
Edit: Yes, fares on easyJet or any budget airline are cheapest if booked months in advance and fairly expensive if booked at the last minute. Fares keep going up as more tickets are sold.
If your plane were late getting to Heathrow, causing you to miss the strict check-in deadline which all budget airlines have, your ticket would be worthless. You would have gone through the time and effort to transfer to another airport, all for nothing.
If you're worried about BA, you could check fares on BMI. There is a flight that leaves Heathrow for Amsterdam at 10:30.
Or stick with your original plan, use your railpass, and take the train. The pass gives you flexibility, which will work in your favor if you're late arriving at Heathrow.
