You were OK using the 30-06 gauge for the 338-06, the chamber headspace/ cartridge head clearances are the same for both, but its not for the improved 338-06 Imp. They're a unique length, head to the point they contact the neck-shoulder junction, the '06 Go is .004"-.006" longer at that point.
Speaking strictly improved rimless bottleneck cartridges, the head clearance (or the lack of it) on the parent in an improved chamber is established on the neck- shoulder of the parent with a crush fit for firing-forming, not on the shoulder.
As the neck diameter increases/decreases the length from the casehead to neck shoulder also increases/decreases, the 308 family for instance.
To do it right you'll need to get an improved gauge or shorten the '06 Go .004"-.006".
Bill
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