Barry's conclusion matches what I've seen too — there's no way to add a "1 inch = 60 feet" entry to the built-in scale list. Custom scales are stored as plain ratios (1:720), and the title label is auto-generated from that ratio, so a custom scale can never carry the feet/inches wording on its own. The practical fix is to leave the view's scale alone and override just the label:
1. Keep the view itself on the custom 1:720 scale so the geometry stays correct. 1 inch = 60 feet is exactly 1:720 (60 x 12), so the drawing is right — only the text needs changing.
2. On the layout, open the title object's settings and switch off the automatic scale display, then place plain text reading 1" = 60'-0" next to it. Save the title as a favorite so every 1:720 sheet in the project stays consistent.
3. One caution: the manual label won't follow the view if someone changes the view's scale later, so it's worth a quick check before issuing — or a note in the office template.
Changing working units won't get you there either, by the way — it only re-words the same auto-generated ratio (e.g. 1"=720" vs 1 Foot = 720 Inches), since a custom ratio has no way to express "1 inch = 60 feet".
I usually double-check with this free scale converter: https://gad.design/scale-converter
