If anyone is interested, I modified the "all paralogues unlocked" GameData.bin.lz to also unlock the 4 hero battles, so you can actually do those and recruit the character with their weapon, as well as adding the entry to your logbook. (You will have to edit your save to remove the shield if you want them to support, though.)
Note: I'm not super familiar with the gamedata.bin layout so I -may- have screwed something up, but I only changed 4 bytes so it SHOULD be ok, but just as a warning!
https://mega.nz/#!WIAGDDhQ
edit: Also, just fyi, you need to be on chapter 8 (paralogue 1 unlocks) for all the paralogues and hero fights to unlock.
edit2: If you go the other route, I wrote some instructions on how to hex edit your save to add in the 4 hero weapons that you can find in the OP here:
http://gbatemp.net/threads/fe-fates-a-way-to-unlock-hero-battles-without-amiibo.418795/
One route requires you to hex edit weapons in, the other requires you to hex edit the shield icons out. Neither is perfect, but at least we've got options!
edit3: I don't suppose anyone has a list of the stat modifiers the 4 amiibo characters have as parents? D: edit5: serene's forest was down when I posted this, they have the data on there! edit6: Any reason Ike/Robin/Marth get the short stick in S supports?
Really wish I had a better understanding of the support tables so I could adjust stuff myself. Maybe I'll tinker around this weekend
edit4: Seconding issue with placing defenders causing the game to crash.