You missed one piece, though even with that you'd probably not be happy.
For each full time increment
spent moving, the character must rest a number of rounds equal
to ((20 – Con Bonus; minimum of 1) x Pace Multiplier).
The time increment for walking is hours, therefore for your example it should be 9x ((20-9)*1) rounds or 198 seconds = 3' 18"
Your Con bonus of 9 means that they have a 91-95 Constitution. This is no normal grunt soldier.
Also, it is a walk pace and not a training forced march. For that consider using a 1.5 pace multiplier and reduce the time increment to 30 minutes per Con. Making this adjustment you get a max forced march of 4.5 hours without rest, and then a rest period of 9x((20-9)*1.5) rounds or just shy of 5 minutes.
The formula is not intended to be fully realistic as there are numerous other factors out there that could change the calculation - but HARP is not intended to be that complex. It's meant as a rough guideline (and I would only use it for the high pace levels) otherwise BMR will breakdown. The biggest issue is a lack of encumbrance rules impacting that since even at 120 pounds of extra weight there is still nothing to prevent your character from walking for 9 hours at no reduction to movement speed and no additional rest required.
So yes - there is an issue with the realism of that formula in that application and no - it is not likely to be changed because there is no need to add extra complexity.