What are the best recommended certifications, outside of NET+/SEC+/A+ for signal soldiers to earn?

The certs you mention are only the basics needed to be MOSQ'd. If you want to go beyond for professional and civilian career purposes, you should start with CCNP/CCNA, MTA/MSCA/MSCE. If you want to move into cyber-security, then I would suggest CCNS, CASP, CISSP.

DoD 8570.01-M is a good reference to start with.

It really depends on where you want to go. Network? Cisco/Juniper/Palo Alto Networks. (I hold a CCNA and am working on my CCNP.) Systems? MCSA/MCSE, Linux, ETC.

ITIL is a good one to start as it covers the processes in all of the IT Industry.

Bottomline, if you have the ones earned through CompTIA, its time to focus on vendor specific.

Network+, Security+, CISSP and CISA