Tightening the diamonds should help, but then the main probably isn't cut for prebend. Swept-back spreaders are another typical upgrade, but then, you'll still need another main cut for the prebent mast. Frankly, your best investment would be in a new main and a decent boom from the sound of it.
HM stands for "high modulus" http://en.wikipedia.org/wiki/Ultra-high-molecular-weight_polyethylene ,and yes, Kevlar is one example
Is your main loose-footed? I've never seen a Sq w/o an outhaul.
Here's a pic of something like I had in mind.
the difference for you is that you'd make a loop of HM line thru the clew round the boom, provided it's a loose-footed main. This is instead of a car and track and what will hold the clew to the boom. Also, from the clew to some point forward on the boom, you'd attach a bungee so the clew will come in automatically, as it were. If your boom is rectangular, as is mine and all the other stock Sq I've seen, the loop round may not run as smoothly as you might like and you might have to rig something different. But it's easy/cheap/simple to see if that works for you.
The Formula 18 cats have something similar although their booms are simple carbon tubes. You can find something like an old windsurfing mast etc to use to fabricate same.