Hey Matt,
Yeah, it's a real hair puller. My answer was a trial by fire solution. I'm pretty clueless about the details. The things I wanted -- a significantly faster site with W3TC, forms that worked, and theme features that worked -- were achieved by this solution ... but HOW is beyond my little brain's comprehension. Minify is enabled, is manual, and I have exceptions for just GF and a couple of js files that affect Google Map display in my theme. Because the exceptions work, I assumed that the minimizing is working. That may be a pretty big leap, in hindsight.
Here's my settings specifically, again with the main "manual" set first:
Rewrite: checked
Disabled: checked
HTML minify settings: Enabled
Inline CSS minification: checked
Inline JS minification: checked
Line break removal: checked
js minify: Enabled
CSS minify settings: Enable: checked
Preserved comment removal (not applied when combine only is active): checked
Line break removal (not applied when combine only is active): checked
ADVANCED:
Update external files every: 216000 seconds
Garbage collection interval: 216000 seconds
Never minify the following pages: <complete URL for GF folder inserted here>
Never minify the following JS files: <complete URL for two js files inserted here>
I hope this helps but, if not, post your own settings here so that some passing person with greater W3TC knowledge might be able to find the solution!