"Yes, definitely build custom crypto for your single signon system, especially if you think HMAC is an "encryption" but just "not as secure" as DSA because it's "shared secret"."
SSO schemes are one of the primary reasons people build crypto for their web apps (they don't want the database dependency between the shared apps). These schemes usually fail calamitously, sometimes a year or two into production, when your app coughs up the ability for one person to log in as any other person without a password.
If you have a real app with a real customer base or doing real revenue and feel the need to put something like this in the field, please ping me. I'm not going to try to charge you. I may try to talk you out of it, though. I will absolutely talk you out of using RSA or DSA.