Based on a combination of the info provided, some on-line research, some familiarity with two MY2000 F250 4x2s (one a V10, the other a 5.4), and more recent experience with a 2017 F350, a 2019 F350, and our slide-in camper, I frankly think you have more to consider than just which gears to get. But, let's start there, and then I'll address some other issues.

In short, I'd suggest getting the 4.30 gears to replace the 3.73s. This ratio was a factory option in 2000 (I don't have 1999 specs), and it increased the GCWR for an F250 V10 4R100 from 17K lbs. to 20K lbs. The 4.30s should help acceleration from a stop (due to 4R100's long 2.71:1 first gear), help overcome the camper's significant aerodynamic drag, and also help with high-altitude performance (thin air = lower HP). They'll also help a bit with the 265/70R18 tires, which are ~3% larger than the original stock 235/80R16s or 265/75R16s.

The described combination of truck, camper, and trailer will likely result in low fuel economy. To limit transmission hunting, lock out fourth gear, which will allow third gear to lock up the torque converter and help the transmission run cooler.

Here are some other issues to ponder:

I'm assuming your truck has an 8' bed, but the cab configuration (regular-, super-, or crew) isn't known.

The 1999 F250's GVWR was 8800 lbs. Allowing for a present-configuration truck curb weight of perhaps 6000 lbs., that leaves ~2800 lbs. for the camper, you, and any other passengers, tools, or other cargo. A CAT scale weigh of the truck will provide accurate numbers.

The camper's wet weight of 3,600 lbs. – which doesn't include the driver or other stuff in the cab – far exceeds this estimated payload value. The larger tires (3195 lbs. each load capacity at 80 psi cold) and axles are probably OK, but this payload will easily bottom out the F250's stock rear suspension. So, you may need to look into a rear suspension upgrade, perhaps something like the springs from a 1999 F350.

To put this in perspective, I wouldn't begin to consider carrying a 3600 lbs. camper on our 2019 F350.

If your truck isn't fitted with the optional camper package, then you may want to consider installing a rear anti-roll bar. Check with Hellwig.For a camper that weighs 3600 lbs., I'm assuming the 13' measurement provided is for the floor length, and not the overall length. Check the camper's center of gravity spec to make sure it's ahead of the front axle.

Does your trailer have brakes? If not, the truck's stock brakes may have trouble controlling ~14.5K lbs. on long/steep downhill runs.

What kind of tie-downs and turnbuckles are you planning to use to secure the camper to the truck?

Finally, you mentioned a CHP scale. What will happen when then the CHP weighs your loaded truck (truck + driver + stuff + camper +trailer tongue weight) and finds that it exceeds the factory GVWR?

I really do hope this helps, and I wish you the best of luck with your NPS adventure!

Regards,
Jim / crewzer