We have done the London / Paris combo multiple times, always rely on Eurostar, and we have an open jaw flight schedule from the US via LHR and CDG. Our favorite way to do this combo is we fly to Paris first - then at some point Eurostar to London - then London to US, and whichever order we do the cities, we have not and would never count on Eurostar for a same day transfer from either city to catch a flight home as you first asked about. So our Eurostar trip always take place somewhere in the middle of our trip abroad, allowing for disruptions that, while a nuisance, have nothing to do with missing a transatlantic flight connection and being on the hook for that cost.
So given that you already have your roundtrip air to/from LHR, plan to return to London at least one day prior to your LHR flight home. For future reference, open jaw is the way to go, though. While taking the Eurostar is a nifty way to connect between London and Paris (or vice versa), I would not rely on it for a round trip connection myself given the vagaries of train strikes and other disruptions.
All else being equal, I prefer taking the Eurostar FROM Paris to London rather than the other way around. Why? Getting to the station and processing through security seems easier / less hassled in Paris, for one thing, and I also find getting to LHR from central London for a return flight home is "easier" than getting out to CDG from central Paris on the morning of a flight home. These are personal preferences, but they are based on having done this many times before, so YMMV...