It might actually not be that crazy.
Start with 16 in both Dex and Con.
That’s gives 16 AC
Graceful Cloth + 2 Dex - 17 AC
ASI + 2 Dex - 18 AC
ASI + 2 Con - 19 AC
Braces of Defense - 21 AC
And if you really want to there is more gear to improve armor class.
I don’t know if any light armor can match that. You’d have good AC and plenty of HP. Might not be the worst idea.