I agree. Last time I parked in the value lot, finding a spot was a real challenge. Your best bet is late at night.
I have looked into free parking options. Not for the faint of heart, and definitely not for long stays, but here goes:
- at T3, there is a credit union opposite the 4Points which has open access. I parked overnight during La Nuit Blanche (mattress run) & did not have an issue;
- the Congress Centre (further up Airport Road) has huge parking lots and limited overnight activity. I parked there last year (near the CBSA facility) and - again - no issue. Behind the building, there is a GO station, which is another option!
- opposite the Sheraton Airport Hotel & Conference Centre (Airport Road), there is a road which leads to the highway. If you take it you will find free street parking on your right (I park at the bakery as there are many ees who also park overnight);
- my personal fav is to pay for an overnight stay at the Hampton Pearson Airport. The breakfasts are decent, and they give you a parking pass marked with your return date (last time, they did not charge, but if its 2 weeks, they may have an issue!).
If you have a buddy who works at one of the buildings on the airport strip, ask him/her if their office is closing and if so, can you use their parking spot! There are tons of spots, but most of them are signed as permit parking only.

The lack of free parking near YYZ is a bit of an issue. LGA has it, so does ART, OGS. One more reason to cross the border..........