If you are set on the 5 foot separation, and your grade is going to be "off-scene" (out of sight?) then I agree with Jeffery that your best bet is a helix.
If it is visible, remember that the prototype would have been using similar trackage to your calculated 17 switchbacks (maybe not quite so many, since logging lines would use up to 10%). After all, you are trying to climb about 450 vertical feet.
For comparison, a "regular" line might allow 130 feet rise per mile (~2.5%), so would need about 3.5 miles to make the climb. That's over 200 feet of scale track in HO.
Andrew