Does anyone make larger torsion spring clips for recessed lighting fixtures?
As DIY springwinding goes, that's a pretty easy one to start with - you can get a pack of 100 12" long spring-steel wires (straight, not a coil - it will be easier to start from there) and put the central coil and end bends into them. Bend around a smooth metal rod, and you'll have to bend somewhat past where you want them to end up, due to spring-back.

Then again, you could pry (or unscrew, but I'm guessing it's pry without being able to see that) the mounts out of the joists and lower them before remounting.

I'm not seeing extra-long torsion spring clips when I search for them; that does not mean they don't exist, but it doesn't mean they do, either.