I'm not sure that this will help :
I have created my own chord symbol library (it takes a couple of hours, but at least I get what I like, and I have loaded the library in all my templates), and, like you, I prefer to use ø. I thus have created that suffix, and I'm able to use it without any problem.
For your info, on my Azerty (French) keyboard, that symbol is available under opt-zero (opt is also alt on the Mac), but I have it in Maestro and you will have to find the correct slot for your set up.
If you cant' find the symbol in Broadway, you can create a chord suffix in which the ø is in another font (Maestro, etc...). Each element of a chord suffix can use a different font.
MacOsX 10.11.6, Finale 2014.5, 2012c, Mac Mini Intel Core i7 2,7 Ghz, 16 Go Ram, Dolet 6. Azerty kb. Full TGTools. MOTU Midi Express XT USB, Roland Sound Canvas SC-88vl, MOTU Audio Express.