I have looked into this in the past and it's very disappointing how insecure this functionality is in general. The only specific additional security I could find was the Amadeus PNR Security Element which states this:
PNR Security
Amadeus individual pnr security allows you to set up special security
rules so that a pnr can be accessed by one or several other offices.
The PNR security functions may allow access to a PNR even when there
are no other special agreements in place and can override agreements
that are contained in the current security tables. PNR security
allows you to share PNR viewing and/or updating capabilities, without
changing PNR accordingly.
Creating a pnr security element
The individual pnr security element is an un-numbered and can only be
created by the responsible office.
R = For read only access: it is
possible to view the pnr, but no updates are allowed. In this case the
agent is given an error message at the time any pnr update entry is
attempted.
B = For both read and write access: full pnr update is
allowed, except for change of ownership.
N = For no access: the
office id specified cannot retrieve this PNR via extended security
agreements. (This overrides EOS)
Office IDs can include wildcards.
To enable this, it sounds like you'd have to book via a trusted travel agent who could set these specific GDS parameters for your PNR.