Tim.........
I live just a couple miles off the Trace, just outside a small town by the name of Raymond. If you have a map, you should be able to reference where I'm talking about.
Anyway, though it appears from your post you plan to spend maybe 2 days on the Trace, I have no idea of what preference you have w/respect accomodations. So, as a convenience, I can only recommend cabins located at Trace State Park, Tishamingo State Park and J.P. Coleman State Park. You can certainly google up those locations for contact information. The only problem may be timing, as cabins at these locations are in high demand on weekends, and since you are less than a month out, I suspect you might have some booking issues. Since the 18th is a Thursday, you might be ok on that date, but the 19th...............hmmm.......you'll just simply have to try and see what you can do, maybe you'll get lucky. J.P. Coleman is the only one not actually on the Trace, the other 2 have direct Trace access and are comfortable, reasonable priced accomodations.
Now, as far as elevation goes, you'll only be a couple hundred feet above sea level, until you begin reaching NE MS and even then, your not going to raise any significant elevation. Mid September can be hot especially at the southern/central sections, maybe a little more comfortable toward the northern section........at least the humidity should be somewhat less up toward that section.
Do not consider riding the Trace at or before sunrise, nor at dusk or after dark. Deer are rampant and your odds of making it through are diminished.
Being unaware of your schedule, if you have time and want to see some of the sights I can only suggest maybe Vicksburg Military Park, Port Gibson, MS, Windsor Ruins, Grand Gulf Military Park and Raymond, MS. All these locations have some significance w/respect to Civil War history, if your into such things. All locations will take you off the Trace to varying degrees, but if you have not seen these things, and if your schedule allows they are all worth seeing. There are some nice MC riding as an added benefit.
At Port Gibson (the town/port where Grant exited for his seige of Vicksburg) is noted for its beauty, the town that Grant refused to burn. There you will take Rodney Road, it will take you to Windsor Ruins. A very nice MC ride!! shady, curvey relaxing, etc. After there you would head back to Port Gibson, then head N on hwy 61 just a couple miles N of Port Gibson, look for signs that take you to Grand Gulf Military Park. After visiting there, reverse your route back to Hwy 61 and go straight across the hwy, this puts you on hwy 462 also known as Old Port Gibson Rd, (the route which Grant marched his forces on his way to Vicksburg) a very fun curvey MC ride indeed! This will take you to the Town of Raymond. In this town was the Battle of Champion Hill, the courthouse was used as the hospital for Confederate Troops and the Catholic Church just a couple blocks down served as the hospital for Union troops. There is a confederate cemetary here as well. You can access the Natchez Trace north of Raymond via 467. Keep in mind that Old Port Gibson Rd runs parallel w/the Natchez Trace and there are several areas along this route to access the Trace if you so desire. Living here, however, I have ridden the Trace countless times that it's a bit boring to me, pretty........yes.........but boring none the less, speed limit is only 50 and it's a pretty straight relatively flat ride. Old Port Gibson Rd (462) is much more MC friendly, curvey and just fun to ride. It is my go to pic/favorite local ride for Saturday afternoons when I have a itch to ride local.
Anyway, it's easy to find these routes if you have a GPS or use Google maps, it's a simple process and it pretty much takes you along parallel w/the Trace so your not far off your intended route...........just an alternative suggestion.
Good luck, the Trace is a very nice ride if you've never done it before, don't let my opinions referenced above deter your rides/thoughts/plans as I enjoyed riding the Trace very much when it was all new to me, it's a beautiful ride for first timers, but remember to respect the deer............and the police............remember this is a federal parkway........those guys mean business!! they normally give you a couple miles over, but watch the speed limits close because they drop suddenly in certain areas and that is usually where LEO lurks in waiting.
Have fun, be safe and I hope you enjoy your trip.
Regards,
Bruce
Edit: I see now that you plan to camp...........if that is the case you should have no problems camping at any of the state parks mentioned above.