Thanks for your helpful replies. Here are some examples—all sold as tachi—of what I find confusing, or at least not consistent:
Tokubetsu Juyo from mid-Kamakura (~1299), 72 cm, o-suriage, papered as katana (I assume because of the o-suriage?)
https://www.aoijapan.com/tachi-mumeirai-kunitoshi/
Tokubetsu Kicho from early Muromachi (~1398), 71 cm, ubu (?), papered as katana
https://www.nipponto.co.jp/swords6/KT332998.htm
Juyo, mid-Kamakura, 73 cm, suriage, papered as tachi (meaning dai to)
https://katananokura.jp/SHOP/1203-TC01.html
Juyo, Nanbokucho period (~1362), 71 cm, ubu, papered as tachi
https://www.sanmei.com/contents/media/S35492_S830_PUP_E.html
Tokubetsu Hozon, late Nanbokucho, 75 cm, suriage, papered as tachi
https://nihontoart.com/shop/tachi-signed-akikuni/