One alternative you did not mention is buying a used cyclo cross bike and adding a rack. They have the right geometry and many have the right braze ons. Check on a used Surly Cross Check for example. A used older mountain bike with a rigid fork can also be had for under 200 dollars and easily modified to do the job plus it has the right gear ratios already. I recently reconditioned an old Jamis Diablo for less than that for off road touring. Don't let the equipment choices stop you.