Clamping halves of a core blank, or anything similar, is made much easier by using a simple “4-way” clamp like the ones pictured here. I use the WoodRiver Clamping System which can be bought from Amazon or places like WoodCraft. You’ll need six or seven of them to clamp up a core, so look for them to go on sale.
These clamps can be made to fit any size panel you wish to glue up since you provide the wood portion of the clamp. The clamps won’t close all the way, though, and they often wont close far enough to make contact with the face of a normal core blank, which is fairly thin. You likely need to use spacers to make up the extra thickness. I use a few pieces of one-quarter inch hardboard with packing tape to prevent the glue from sticking to them.