While trying your suggestion, I may have stumbled on the cause of my problem. I modified the .pm file as you suggested, and ran my test file. The library paths were printed as you'd expect, but the library still did not load. I wanted to be sure the library was actually where I specified, so I cd'd to that folder and did a directory listing. Then I ran the test file again, and the library loaded!!
WBBirkett-M:perl5 wbirkett$ cd ~/
WBBirkett-M:~ wbirkett$ perl -I/Users/wbirkett/Library/Application\ Su
+pport/TextMate/Pristine\ Copy/Bundles/PressCal.tmbundle/Support/lib/p
+erl5 /Users/wbirkett/Desktop/Rmath_test.pl
XXX=/usr/lib
XXX=/usr/local/lib
XXX=/Users/wbirkett/Library/Application Support/TextMate/Pristine Copy
+/Bundles/PressCal.tmbundle/Support/lib/perl5
Can't load '/Users/wbirkett/Library/Application Support/TextMate/Prist
+ine Copy/Bundles/PressCal.tmbundle/Support/lib/perl5/darwin-thread-mu
+lti-2level/auto/ICC/Support/Rmath/Rmath.bundle' for module ICC::Suppo
+rt::Rmath: dlopen(/Users/wbirkett/Library/Application Support/TextMat
+e/Pristine Copy/Bundles/PressCal.tmbundle/Support/lib/perl5/darwin-th
+read-multi-2level/auto/ICC/Support/Rmath/Rmath.bundle, 1): Library no
+t loaded: libRmath.dylib
Referenced from: /Users/wbirkett/Library/Application Support/TextMat
+e/Pristine Copy/Bundles/PressCal.tmbundle/Support/lib/perl5/darwin-th
+read-multi-2level/auto/ICC/Support/Rmath/Rmath.bundle
Reason: image not found at /System/Library/Perl/5.18/darwin-thread-m
+ulti-2level/DynaLoader.pm line 194.
at /Users/wbirkett/Desktop/Rmath_test.pl line 1.
Compilation failed in require at /Users/wbirkett/Desktop/Rmath_test.pl
+ line 1.
BEGIN failed--compilation aborted at /Users/wbirkett/Desktop/Rmath_tes
+t.pl line 1.
WBBirkett-M:~ wbirkett$ cd /Users/wbirkett/Library/Application\ Suppor
+t/TextMate/Pristine\ Copy/Bundles/PressCal.tmbundle/Support/lib/perl5
WBBirkett-M:perl5 wbirkett$ perl -I/Users/wbirkett/Library/Application
+\ Support/TextMate/Pristine\ Copy/Bundles/PressCal.tmbundle/Support/l
+ib/perl5 /Users/wbirkett/Desktop/Rmath_test.pl
XXX=/usr/lib
XXX=/usr/local/lib
XXX=/Users/wbirkett/Library/Application Support/TextMate/Pristine Copy
+/Bundles/PressCal.tmbundle/Support/lib/perl5
OK
So, the failure to load the library is somehow connected to the current directory in the Terminal app. I don't know why that would matter, but it looks this is a macOS problem, not a Perl problem.
Thank you again for your help.