What, if any, online tools do y'all use to plan itineraries?

I'm currently trying to plan something along the lines of LHR-NCE-IBZ-MAD-LIS-OPO-LGW in August for 2 pax, where:

• LGW-NCE could be substituted for LHR-NCE, if more economical. No LCY-NCE though.
• LIS-OPO could also potentially be OPO-LIS, if more economical
• LIS-OPO (or OPO-LIS) would be a surface segment (hire car)
• LHR-NCE and OPO-LGW (or LIS-LHR) are BA J (either booked J, or Y + POUG if silly money)
• All other segments are IB Y (no I2 though, as keen to get Avios+TP)

With a lot of moving parts and possible options, and not that fussed with specific dates (but pretty sensitive to price), I'd want one place where I can plan and budget the whole itinerary (even if the flights themselves are booked separately), see the whole trip in one overview, see the total cost, and see how jiggling different dates and routing options affects the price.

All the usual travel sites have a multi-city option, but they want specific dates for each segment, and then come up with a random mix of Ryanair and easyJet and no flexibility at all to refine before the algorithm gets confused and throws its toys out of the pram.

It's clear this needs to be booked in many separate bookings, which I don't mind. But I'm going mad trying to keep it all straight, and every travel site there is seems to prioritise sales conversion tactics over usability, so I have no place (that I know of) where I could plan and budget efficiently.

• BA.com in my attempts doesn't want to sell any IB flights at all; they want to sell an LHR connection for all the internal segments
• Kayak has a "Watchlist" I can save to, but the second I start searching for the other segments, the previous ones are automatically deleted for my convenience
• Expedia allows you to "save for later", but since I'm searching for each flight separately, it creates a separate itinerary for each flight, and I can't find any way to merge them.
• TripIt would require a LOT of manual typing and fiddling.

So, what do the fine girls and boys and others of this board use to plan, price and fine-tune complex itineraries like this?