I've replaced all the flooring in my house with hardwoods, and now I'm having trouble figuring out how to make the baseboard and shoe molding meet the existing cove molding around the hearth/fireplace:

Here's the dimensions of the moldings:

baseboard 3 1/4" tall x 9/16" thick

shoe 7/16" thick

cove 1-1/4"x 1-1/4" footprint, edge is 1/4" thick

This is what they look like butted up. Obviously I can't just have the baseboard end at the cove molding.

I'm not opposed to cutting off the bottom of the cove molding and adding a plinth, but I can't find a decorative one that's the right size and I think a plain piece of pine will look unfinished. Looking for any fresh perspectives that won't look like an afterthought! Thank you!