I ended up concluding it's easier pushing the GOP to move to the center on economic issues than to pushing the Democrats to move to the center on social issues.
Look at what the core philosophies of each party have been since their respective foundings and you'll find that it is precisely the opposite of what you've concluded*.
*Except for that socialist fling the GOP had in the 1860s; paging Yankee's anger!
The core philosophy economically of the GOP, has been what its allied business interests want. When that was protectionism and infrastructure, it wasn't hard to find socialists to take along for the ride on such a nationalist program.
Keep in mind the politics of Germany following its unification as well and remember that the GOP had significant intellectual influence from German economists. Conservative elements allying with Socialism or at least coopting it to keep radicals from tearing the old systems and aristocrats limb from limb, was present in many places.
