I know that NASCAR 5.9 liter V8s use crossplane cranks in them, due to rules, and that flatplane V8's over 4.5 liters tend to have problems with destructive vibrations(Ala, Cosworth DFV, which was a 3 liter F1 engine). But is it true that the engine builders modify the crankshafts, namely in that they use a trick that my father(who used to build dirt late model engines) mentioned, which is that teams cut most of the counterweights off of the crank before it's installed? And wouldn't that cause vibration issues, as crossplane cranks need heavy counterweights to smooth out side to side vibrations?

Here's a picture and a description of a crankshaft from a Chevrolet R07. Billet steel by an aftermarket supplier. The counterweights are smaller than those found in a conventional small block Chevrolet engine, but are still substantial. Polished and tapered at the leading edge in the normal manner. The R07 has its camshaft gallery isolated from the crankshaft in order to prevent oil from falling onto the spinning shaft.

http://www.fullthrottleusedparts.com/servlet/the-198/BRYANT-SBC-R07-BILLET/Detail

Cheap deal if you happen to have an R07 block and heads kicking around.

The old saying "If your engine blows up as you cross the finish line, its done it's job," applies.

Short duration race engines will have lighter rotating/reciprocating components, just because they can. Engines that experience major RPM transients during a race will have lighter components in order to reduce the rotational inerta. Full on oval engines that run WOT for extended times will have full counterweighted cranks to cut vibration, and those weights will be heavier to balance the heavier rods and pistons as well. The cranks that really get shaved are the short track cranks where you are constantly on and off the thottle, and have relatively short heats on race day. SOP was to cut the center counterweights completely off and use the smallest diameter flywheel as possible, and machine the flywheel until you could see through it. Once you cut the center weights off a crossplane crank it ends up with about the same vibration as a flat plane.

Some of those short track cranks with rifle drilled journals, and thinned counterweights, look so fragile. You get lots of vibration and harmonics in a setup like that, but hopefully the race is over before you beat everything on the bottom end to death.