Bill,
You would have to use a bullet that is no LONGER than
1.25" long for full stability in the 18 twist barrel. 
The Length is the most important factor regarding stability.
The weight "just comes along for the ride". 
A friend has been campaigning his 18 twist 40-65 with a 1.25" long, 380 grain DualDiameterPaperPatch bullet in BPCR Silhouette matches for a couple years with success. They shoot out to 500 meters. This is his most accurate BPCR rifle. 

On the other hand, if I were to build another 40 cal rifle, I would use a 14 twist barrel for most universal use, especially if a person wanted to shoot long range as in 8,9,1000yds.
beltfed/arnie

I agree that the 1:18" twist is likely going to work best with bullets under 400 grs., and I've had great results with the RCBS CSA 350 gr. in my .40-70 Ballard, and .40-85 Ballard rifles with old slow twist barrels.
I am not sure there's any advantage with a 14" twist over a 16" twist myself. Having owned two rifles in the exact same .40-65, and both with Green Mountain barrels in each twist rate. Both being built on Rolling Block actions.
I couldn't see any difference in accuracy at 1000 yds., when trying a variety of bullets from the 350-420 gr. weight sizes. Putting them on paper to get a better idea of which was better, neither shot smaller groups over the other.

I had to drop down to the 370 grain Saeco (#640) to get good results in my 18 twist 40-60.

Thanks fellas. 
Westerner, can you tell me what bullets have performed well for you in a 1:18 barrel to 1,000 yards?

Area of Sea Level and Altitude of Density can also play its own part.

Totally agree if you are not up to serious competition none of it really matters anyway!

Bill,
I've been dabbling in the 40 calibers lately.  I have a Hepburn I built with a 1:18 twist 40-82 Win and never had an issue with the build at a 1000 yds. the problem is always the guy jerking the trigger. 
I recently built a 40-70SS  with a 1:16 twist - as I mentioned in a recent post - used it in a mile match.  The wind messed with me some but it wasn't bullet instability so much.   
I've attached a PDF with stability calculations using Miller's formula.  Both bullets are longer than most use.  One is from a Baco GG mold and the longer is from one of mine - a paper patch mold.  The first two are calculations for a 1:16 and the second two are for a 1:18.  All of them are well within the recommended numbers. 
my 2¢
Greg