don't throw solutions with confidence like they are silver bullets. spiped is unmaintained, doesn't support revocation, not easy to debug in a big infrastructure, and will require a lot more work compared to https + client cert authentication, and doesn't provide multi platform support.
PKI is used to build a chain of trust. Whether it involves third parties or not is not the point.
TLS is the right solution iff you need to communicate with third parties whom you can't securely share code or keys with in advance.