OK, so we’re talking about the same piece of wood. I would definitely not try to fix the channel (the “mortise”) directly onto the fibreglass. Use a hardwood packer, either made in advance, or, if you prefer, made after you have fitted the mast plug (with the “tenon”), which gives you a second chance to adjust the precise height relative to the pivot hole. The packer should end up at least 15mm thick so as to have enough intrinsic strength that it doesn’t split.
If you’re not too confident with a hacksaw, just cut off a bit less than you calculate that you need to, then file off the rest. But this will quickly become tedious! With a new blade, adequately tensioned in the saw’s frame and with small enough teeth – look for a high tpi (teeth per inch) figure; at least 24 – you should be able to make a good job of it. I would use some tape – electrical, masking etc. – around the mast as a visual guide for the cut, to ensure a nice level result, but there’s always the file to tidy up any burrs. A half-moon file will tidy up the inner edge nicely if you have (or can borrow) one.
I’m sure I don’t really need to ask, but the new plug does fit the mast profile?