Bikes on trains in Spain seem a no-go, but are totally okay in Portugal.
The very simplest might be to use your bikes from Santiago down across the Galicia/Portugal border, then train with bikes to Lisbon, then take them on your flight. Portuguese trains will not require you to break down your bikes. Quite a lot of them have specialized carriage spots for bikes.
I think shipping them unaccompanied Spain>North America will likely cost at least half the price of the bikes--unless they are valuable ones.
The other thing you could consider, if they are NOT extremely valuable, is just donating them to someone in Santiago; I'm sure there are those who could use them.
I concur with the statement above about trans-border car rentals. Even if allowed, they're quite pricey because you're doing a one-way rental with a drop-off fee.