Great plan! September a great time for departure. You will have no problems with tires, just plan your changes carefully. Most of S. America you have limited choices ... so expect compromise.

Obviously front tire will last double rear tire, so a good front that works well ON and OFF road is ideal unless doing mainly ROAD travel. But traveling out of USA, longevity has to be TOP OF THE LIST.

Of 10 or so different fronts used on my DR650, my two favorite front tires have been TKC80 and IRC TR-8. The TR-8 lasts longer, cheaper and works a bit better off road, the TKC80 works very well ON road, excellent handler for knobby tire, even in wet, expensive, good for maybe 7K to 9K miles at most. (in my experience)

Way back in 1998, rode a new 1998 KLR press bike from San Fran Bay to Baja, Copper Canyon, lots more. 6600 miles, 6 week tour. Stock Bridgestone rear worn out by Durango, Mex. (under 3K miles!) Found a funky Kenda road tire that fit, ran that rest of the way.

Rear tires are more of a challenge once traveling. I like the D606, used them front and rear in Moab, UT and Colorado passes. Very good if mainly OFF ROAD ... but the rear lasts maybe 3000 miles, bit more. Front lasts but slippery on wet pavement.

Lots depends how much off road you want to pursue. When in US you can re-new your tires anywhere anytime and quickly. But once you cross that border, tire and tubes are like GOLD.

I often pack a rear tire on the back. Some don't like it, I don't mind. For me, nothing worse than running out of tire middle of nowhere.

A few ideas:
Start with new tires from AK. If you plan to do Moab, Colorado, Nevada Black Rock Desert or Mojave desert off road, then your tire choices should be more off road biased.

Near the border Re-Tire front and rear (no matter if your current tires not fully worn out ... Go NEW!) ... maybe pack a spare rear on the back? Don't forget QUALITY, real rubber spare tubes.

You can find tires/tubes in Mexico or Cent America but you may not get anything any good .. and you may have to wait ... like two weeks. Guadalajara or Mexico City KTM or BMW or other dealers will be your best hope ... and BOY! will you pay big for those tires! Or ... you might get lucky at the Kawasaki dealer!

If you don't re-tire in Mexico then not a whole lot of tires until Colombia. Yes, there are some tires to be had in Cent. America, but few/far between. Remember it's mostly all 125cc or smaller bikes down there.

Once in Colombia you can find tires for the KLR, perhaps not the very best, but
it's getting better. I don't know current details on sourcing tires further South other than they are expensive and sometimes hard to find. Do your research once on the road.

Rear Tire Choices:
Rear tires a tougher choice. Many swear by the German Heidenau, Mefo or Mitas tires. Some seem to last on some bikes but on and off road performance is not better ... or not as good as ... a $60 Kenda K270. They are pretty tough and DO mostly last well. But at $150 a crack ?

For road use I now mostly run the Shinko E705. If you have to go off road, lower pressures down to 17 PSI. The Metzeler Tourance, Avon Distanzia and Michelin Anakee ALL will last longer than the Shinko but at substantial cost.

50/50 rear tires I like:
Kenda K270 (ran over 6000 miles in Baja, Mexico trip)
Surprising off road performance, not so great riding aggressive in the twisties. Only so so in the wet.

Shinko 244 (rear) (Lasts only 4 to 5K miles)
Also very good off road and better than the Kenda on pavement, good in wet. But agressive use will wear it out quick. (I've used 3 on my DR650) Cheap and cheerful but not a S. America tire.

So, key thing is to get from US border to Colombia on one rear tire. The Kenda can do it if you keep highway speeds low. On my trip I ran at 70 to 80 mph in all of USA portions. This took a BIG chuck of miles out of the Kenda. Going slower, I'm confident that K270 would have reached 8K miles.