I also wonder about round length as part of a solution. A round in AD&D, if I recall directly represented a minute of combat. I don't think I'd go quite that far, but if a round of combat represented 20 or 30 seconds instead of 6, with a corresponding increase to the effectiveness of the dash action over open terrain, melee combatants would take a more reasonable number of attacks while approaching combat.
Yes, I think characters are too slow relative to attack rate. Doubling everyone's movement (perhaps through some special Actions like 'sprint' and 'charge' that you can't use while shooting) would help fix that.