Running at 6K all day should be fine, though it will accelerate wear. I would NOT do it.
Your post is unclear, is 5th gear not working, or is the diff ratio just that short?
The head gasket situation sucks pretty bad. You probably did that when you filled with water and kept driving, as it likely overheated enough to warp the head and/or block. You'll basically have to pull the entire motor, have both parts decked, and reinstall. A lot of people swap in a known good engine, but that's even more expensive and not much less work.
I'm not sure what $1K BP works out to in USD, but that doesn't sound like a bad price from what I've seen quoted on this forum.