There has got to be some technique for reefing the mainsail without using reefing points... right?
Actually there are some ways to reef without reef points. The "Fisherman's Reef" comes to mind. Basically this is just sailing with you main sheet sheeted WAY out, making you sail much less efficient and thus reducing heel and drive. I would add that putting your traveler (if you have one) all the way to leeward will increase this effect.
In addition, any sail trim adjustments that you can do to flatten the main will make it less efficient and thus reduce heel and drive, which is what you are going for when you reef. Tension the halyard, tighten up the outhaul and cunningham. Tighten up the backstay. Release the vang to spill wind off the roach of the sail.
If hard on the wind you can "pinch" meaning that you steer too close to the wind, effectively stalling your headsail. This is often done unintentionally by new skippers who over-correct as soon as they feel the heeling pull of the headsail powering up.
It may not be immediately obvious but you should also consider taking down your jib and sailing under main alone. We did this once on a catalina 30 in winds in the 30s in a race. We took down the headsail, and raced under a main that was sheeted way out. This way we maintained some control and PLENTY of power and speed.
Of course sailing under one sail depends on your boat. My old lifeboat-sloop instantly hove-to under main only. You could also try jib only if you have a small jib. (wouldn't try this with a genoa as they are not built for high winds) It has been proposed by some that the rig stresses are uneven and bad under jib alone on a sloop so it would be a good idea to tighten up the mainsheet (even though you have no main up) to balance the stresses.
There is another technique which "may" damage your sails but I've seen it done with success. You lower the main to where you want to reef it and then tie on a single sail-tie at that point, it will act as your clew. It helps if you have a line going from the mast or gooseneck along the boom to keep this sailtie from slipping aft and off the sail. Also if the main is poorly behaved at the luff you can run a sailtie around the gooseneck and tie it to a single sail slide to hold the luff down as well.
This will tie down the main in a reefed position. Since it makes for poor sail shape and stresses can damage the sail in this position it works best down or off the wind as opposed to hard on. I have seen it work well dead downwind though. Probably best reserved for more extreme scenarios.
Also if you are greatly over-powered just remember the lessons of dinghy sailing (as your boat will begin to feel like one) if you loose control let the sheets fly and steer into the wind (or let go of the tiller) and the boat will weathercock itself.
A friend of mine was in a 21 ft sloop in hurricane force winds sailing across the gulf of Mexico once. He had drawn on the reef points on his main and was planning on sewing them in place next week. (If your sail is old I DO encourage you to add your own reef points. Just remember that "sewn on" works better than "drawn on") He did fine sailing all the way across the gulf with main alone and a fisherman's reef (minsheet way out).
Best of luck!