I could give you a several first hand stories of big block Mopars surviving long periods of time (as much as 38 minutes), with no cooling system whatsoever, and winning, or at least placing, in demo derbies.
Not that big block Mopars have anything over anything else, it's just that the big Chrysler cars work very well for demo, and I have used dozens of them over the years.
In every instance, the formula is the same. Heavy high quality synthetic oil (about a quart, to a quart and a quarter over filled, to help increase windage), stock rod/bearing combinations (as they have the oil squirter holes in them to help cool the pistons/cylinders), plenty of ignition advance (not more than stock, but do not block off the vacuum advance, or lock the timing), sufficient octane to eliminate possible pinging (straight race gas does not work well), ever so slightly rich (but not too rich) on the fuel mixture, and a step or two colder on the plugs (may be harder to start when cold, but they work great when hot).
As someone else pointed out, you MUST plan for total cooling failure as it is very rare to keep the cooling system intact and still be running at the end.
Most people make several fundamental mistakes in as much as their game plan wouldn't work on a street car, much less the extremes of demo derby (such as reduced timing, too rich, etc;).
Compression is not a real concern (within reason) as long as you have appropriate octane, as all the engines I have ever run had factory ratings of 10.1:1, which translated out to a true 9.5 to 9.7:1. As with any performance engine, compression ratio is totally meaningless, as cylinder pressure is the only valid measure, and I have found that mid 140's to 150 is ideal for derby.
Though there are many, many other factors that can/will take you out of a derby, just make sure you don't rely too heavily on cooling. In fact you should use an old fan belt and cut it about 2/3 the way through in a couple of places so that if the radiator jams the fan, the belt will break. a nice new belt will probably put you out ... this, and all my other points, were learned the hard way.
Hope some of this helps, and good luck.