Why would you need to regulate power? The geothermal generator regulates power by itself. It produces only as much EU as there is consumption. Once the batbox is full it will only run at 6 EU/t (or more precisely, it will flicker on and off).
The reason you're going through so much lava is simply because the quarry isn't your grandmother's sewing machine, it's a freaking quarry
It does awesome things, but it needs a LOT of energy to run. Also, remember that you're not converting EU to MJ on a 1:1 basis, but rather on a 3:1 basis. Three EU for every MJ produced through the electric engine. You can upgrade the electric engine to be more efficient and only need 5 EU/t instead of 6 EU/t, but other than that? More lava. Or switch to Buildcraft power.
I can see that you have little to no experience with Buildcraft power since you're talking about exploding engines. That's a relic of history stemming from old Buildcraft versions on laggy servers used by people who have no idea what chunk loading/unloading is. Yes, combustion engines will explode if not cooled properly; but, for example the FTB pack gives you no less than 9 different
other Buildcraft compatible engines to choose from. It also gives you the tools to keep combustion engines perfectly cooled while being immune to lag and chunkloading mechanics.
Here's a really simple upgrade for your current system: use magmatic engines, from Thermal Expansion. In your current setup, you get 6666.67 MJ out of 1 bucket of lava; if you upgraded the electric engine for efficiency, you would get 8,000 MJ per bucket. But if you use magmatic engines, they will give you 18,000 MJ per bucket. And all you need to do is remove the geothermal generator, batbox and electric engine, place a magmatic engine in the spot where the electric engine was, and pump lava from the tanks directly into it. Bonus: it runs twice as fast as the electric engine too, so your quarry will dig twice as fast. And it never explodes either. How's that for an upgrade?
There are ways to get even more out of your lava, but those require building completely new power structures; there are also ways of running very efficiently on other fuels, but then you'd need infrastructure to provide those fuels.