The problem isn't really first-past-the-post, although it is problematic too. The problem is the principle of Winner-takes-All of a states electors.
For example, you could vote directly for the candidate, one person - one vote and each vote counts nation-wide. That would drastically reduce the incentive for strategic voting. Of course, the list of candidates needs to be the same everywhere across the country.
The other option is to distribute the electors according to the votes received. If you get 30% of the votes, you get 30% of the electors. Mind you, the electoral system is severely outdated and only ever served a purpose when communication was restricted to horse and carriage. The electoral system should be abolished to start with. The trouble is that neither Republicans nor Democrats want that to happen, because they would both lose big time. Now, their only concern are the swing states.
Lose the electoral college immediately! It is a wasteful and unfair system.