Have you also considered options to fly KLM or Delta / Patrners from other EU gateways? This may also make a difference on cost. You can always book two separate flights to say for your EU and Med haul, and then have the Airline link them in, so baggage checks through. Skyteam partners will always enable this.
LHR is always so dismal to connect, worst rates for luggage missing of any EU airport. I have collected my own luggage and re-checked in many times to avoid previous bad experiences, and the time to queue and travel between terminals.
You may also save over £300 each on taxes, levies, and charges not made from somewhere like AMS?