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Any tips (other than the application of more brute force) on how to
get this tire onto the rim? my thumbs are raw from pushing and I
haven't even been able to seat one bead, fully, yet!

Use your tire lever. Also, make sure that the sections of bead you
have on the rim are in the center of the rim, at the depression near
the spoke anchors, to give them a little room to move as you do the
other side of the rim. Did you put one bead on before putting the
tube in? I always do it that way, though I'm not sure it matters.