Forgot my Snapchat password and have a new number. What now?

I have a ~4 year old snapchat account that I use to keep in touch with a lot of people. There are a lot of close friends that I only communicate with through that app and have no other way to contact.

The phone number I used to sign up with was discarded years ago and there doesn't appear to be any alternative way to reset my password (unless I had signed up with an email, which I didn't).

Am I just shit out of luck? I really, really, really don't want to lose those connections. A lot of them are people I was stationed overseas with while in the military.