Europe - Best way to get around (Paris, Amsterdam, Belgium, London)

Why not fly open jaw London, then train to Paris, Brussels, Amsterdam, then home from Amsterdam. Cuts out all the back tracking and minimizes train tickets.

You can look up the prices and times yourself.
Amsterdam - Brussels - Paris trains are run by Thalys, their website is here: https://www.thalys.com
London - Paris / Brussels / Amsterdam is run by Eurostar: https://www.eurostar.com

In both cases tickets are cheaper if bought early (2-6 months ahead), prices only ever go up. And tickets are only valid on the one train listed on the ticket. The ticket will also show which seat is reserved for you.

I would definitely look for a multi-city flight, either into London or out of London. I think the easiest routing would be:

Fly to London
Eurostar to Paris
Thalys to Belgium (connecting train may be required)
Thalys to Amsterdam (connecting train may be required)
Fly home from Amsterdam.

Or you could reverse the itinerary.

You'd have a bit of additional travel time if you traveled London-Amsterdam-Belgium-Paris or vice versa.

This will be a portion of the trip only and we already used the other 2 stopover that we were allowed on points. Will be going South America and Africa as well. We don't have the option of an open jaw

Assuming you depart from the same place you arrive, I suggest something like this:

Fly into Brussels > Thalys train to Amsterdam > fly to London > Eurostar to Paris > train to Brussels.

This keeps you from having to backtrack on trains. You already have the train websites. Check skyscanner.net for flights.

Look at flights from Amsterdam to London City Airport, close in and with connections to central London on the Docklands Light Rail.