Encourage players to have their characters recall lore more frequently by making the information they can get actually valuable. What that means will be based on the kind of game you run, but knowing the abilities of terrifying monsters, the likeliest locations of treasure hoards, and the backstory of NPCs with whom they must interact can all be very useful.
Include more complex traps that may call for an Intelligence (Investigation) check to figure out. Same deal with figuring out how secret doors work.
Tie the Drawing a Map "exploration task" to a passive Intelligence check and the DC to the party's pace (the faster the pace, the higher the DC). Then make a source map worth gold if they engage in that task to the exclusion of others.
Tie the Navigating "exploration task" to a passive Intelligence check when in a maze-like adventure location instead of Wisdom (Survival).
Some downtime activities like Research can be tied to Intelligence if the task takes place in a library or the like.
In my current campaign, I have a player pool and each player has several characters. So I never know what kind of party I'll have week to week. Last session, I had a party where every character had an Int 8. They were exploring a big, abstract location and they got lost a LOT by not having a decent Intelligence between them. It also meant they couldn't draw a map that was worth anything. So not only did they run into more trouble than they needed to, they couldn't score any easy gold by drawing a decent source map. They were lamenting (and laughing at) their own characters' stupidity by the end of that session.