It bothers me a little that all of your examples are vowels. Especially when you include OSHA in the list of examples. It's not the Shafety and Shealth Administration.
Here's a soft G word making a hard G acronym, and a hard G word making a soft G acronyn:
GAD - Generalized Anxiety Disorder
GEMA - Gas and Electric Markets Authority
Some other non-G examples: PAL - Phase Alternating Line
PAWS - Phased Array Warning System
SWF - ShockWave Flash
They're much harder to find though.