What is max COAL for a “CIP” (not SAAMI spec, but the European agency CIP) spec 338 Lapua Magnum?

The reloading manuals I have all specify “3.681” max COAL.

Even the online cartridge design engineering schematics for CIP 338 LM list a measurement in millimeters that converts to 3.681 inches COAL.

But, here are the AICS magazine specs …

Pacific Tool & Gauge, "Stealth CIP, 3.850"" length, Part # P5664635, A.I. detachable box magazines (CIP length, AICS part # 6715)
-This is CIP length bottom metal, non-standard length
-Magazine box size = OAL 3.850”
-Mag interior OAL of 3.764”
-Fits cartridge case overall length is 3.745”  

This suggests I can load the CIP 338 LM to a max COAL of 3.745”  

Which is it?  And if it’s 3.745”, where is a reloading manual that states that longer COAL?

I use Accurate mags 3.850" CIP mags for my 300 rum..numbers should be similar to yours, my mags OAL outside to outside at the bolt is 3.8550"... OAL inner length is 3.7755",playing with it a bit I settled on 3.760" for coal on a loaded cartridge, this load is on barnes LRX bullets, You need to know how consistent your bullets are from o-give to tip, and adjust accordingly..I have 3 mags, all are almost perfectly identical..I've heard Accurate Mag built good stuff, seems so...
As for yours, you can seat them out as far as you want so long they fit and feed right from your magazines..I dummy seated 5 rounds and tried them in each mag on the rifle to make sure they would feed.. And then when first used, I would load the mag, then feed and fire a round, then check those in the mag for movement(bullet).. zero issues, has worked fine ever since...I load my ELR ammo using the 230/245 Berger hybrid bullets to a COAL of 4.0455"and  single feed them.. The mags are used for up close hunting when needed, basically inside 4-500 yards...

I don't think you're going to find one.

3.681" cartridge overall length is determined by what bullet, and what ogive curve and contact to lands distance?

A maximum cartridge overall length of 3.745" allows magazine feeding -- yet your cartridge can be even longer (say for extra-long range) for single round feeding through the ejection port -- making magazine COAL irrelevant.

3.681 through 3.745 allows handloaders to "Chase the (ogive contact to rifling) lands" as the throat erodes.

This will be determined by the chamber you're shooting them in and, if using a mag, the max OAL of the magazine. There are a couple different cartridge OALs used by different magnum receiver/bolt manufacturers, so you'll need to measure your chamber and/or mags and go from there.

The Hornady OAL Gauges and proper "modified case" make this easy to do and how I found out the OAL I needed to put the bullet 20thou off the lands when handloading.