Curt, I tried to simulate your restore situation. I took a Moodle 2.3 backup, 17MB, and tried restoring it into my low-end hosted server version of Moodle 2.4. My browser showed activity for more than 30 minutes. Never an error message, or any other message. I eventually "Canceled" this, but then noticed that the course was actually installed?
You might try more experimenting. I was not sure if your 150+MB backup included user data, or if it was all course materials. If it contains user data, you might first try resetting this course, do the backup, see if it is any smaller, and then restore it. If you want to preserve user data, create a new course in your Moodle 2.2 from your Moodle 2.2. backup, get rid of user data, backup the "new" course, and see if it restores. You might also try getting rid of any big video files in the "new" copy, back it up, see if it is smaller in size, and then restore it.