Caleb, yes that's the boat.
Yes, I would call it a modified fin keel. The jib is also very large compared to the main.
I've just got a brand new 100% jib, to replace the 150%. The problem with the 150 was that, when reefed to 100% or less, the shape wasn't great. In fact, it was old, so the shape wasn't great ever! So this may have contributed to the behaviour.
Anyway this weekend I'll try heaving to with the new jib, if that doesn't work will try furling it even smaller first.
In reality, you aren't really going to heave to with a 150% genoa in any boat. For your boat, the 100% may or may not work. I'd guess the latter. With a storm jib in a big breeze, then you might be good to go. At that point, the storm jib isn't going to be pressed against shrouds, spreaders, etc... and self destruct.