Is there a way to determine the loader version without going through a manual process? For the purposes of field debuggong I can envision a situation where it may be helpful for an application to have the ability to display this information on a diagnostic screen.

Yes, the application, os, and loader version numbers can be obtained from User Defined Variables that are populated by the System app. So as long as the System app is still running, these variables will be populated.

Here are the specific variables (from MSTD 2.1 Configuration):
UserDefinedVariable.Version.App.1
UserDefinedVariable.Version.App.2
UserDefinedVariable.Version.App.3
UserDefinedVariable.Version.App.4

UserDefinedVariable.Version.Os.1
UserDefinedVariable.Version.Os.2
UserDefinedVariable.Version.Os.3
UserDefinedVariable.Version.Os.4

UserDefinedVariable.Version.Loader.1
UserDefinedVariable.Version.Loader.2
UserDefinedVariable.Version.Loader.3
UserDefinedVariable.Version.Loader.4

There are also version numbers like these in the MSTD 2.0 configuration as well.

The ordering of the version numbers are 1.2.3.4 where 4 is a release label either representing:
Release,
Prototype
Beta,
Development

If you are not running the System application, there are also files placed in the filesystem that contain the OS and Loader version numbers that can be parsed and read. The OS is located in /proc/boot/os_version.txt and /proc/boot/os_version2.txt. The Loader is located in /fs/etfs/nvdata/versions/bootloader.txt and /fs/etfs/nvdata/versions/bootloader2.txt.

just an added NOTE:
Unless you're writing code directly on the PV750 (which some customers are), you don't have any option, the system app will be running.