I'm just an amateur, but here's my two cents. There's more to legato than just overlapping the notes. Using the pedal guarantees that the notes overlap, but does not guarantee that they will be legato. To be legato the volume of each note should match the decayed volume of the previous note (with the common sense exception that you have to find ways to avoid a decrescendo to complete silence in a long legato phrase).
So, if it takes more than a pedal to create legato, then you ought to be able to do staccato in spite of the pedal. So I'd make identical attacks on each of the staccato notes; don't match each one to the decay of the preceding note, just hit them all at approximately the same volume. That should create a staccato effect in spite of the pedal.