You don't say what spine your Beman ICS classics are that shoot well for you, but if they do, go with the same spine on your replacements if the replacements are the same diameter and about the same weight..
.300s are likely too stiff. If you're drawing close to 31 inches, then the .340s will probably be optimal, but I agree that the .400s would also work with less weight up front. If, in fact, your draw is closer to 28 inches, and you just like long arrows, then the .400s would be plenty.
You can probably make any of these carbon spines fly well by adjusting point weight and length (though if you have a 31-inch draw, you don't have the option of adjusting shaft length) and/or the bow side plate thickness.
A compound will shoot anything as long as its overs pined because it's centershot, i.e., cut past center so the arrow can be lined up to bisect the string, and it's shot with a trigger, which just about eliminates fishtailing at the release.