Pirelli says the optimum strategy is two long stints on softs then one super-short stint on mediums at the end. Maybe they have it backwards.
If McLaren are really as uncompetitive on qualy pace as they claim, then maybe they should just run medium tires in Q3 to see if they can get ahead of the occasional Sauber or Williams that eeks into Q3. This would commit McLaren to start on mediums from 8th or 10th on the grid, with two sets of new softs available for each car. Perfect.
Start the race on mediums, change to softs after the first lap, and run two long stints on new softs. They would be ~25 seconds (one pit stop delta) behind the other front runners for the whole race until the other front runners stopped for mediums two laps from the end. I think McLaren would pass most of the front running cars without ever seeing them on the track. The last two laps would be interesting.
This strategy requires quickly passing every midfield car you caught up to. Sounds like a job for Hamilton.