I think the Red Stag taste remains evident and suggests a cocktail because of the amount used, just under 10%. That does not sound like a lot but the Red Stag is quite sweet though. In the 1800's, flavourings were added in different proportions and 10% was by no means unusual.
Still, I looked again at Fleischman for his best bourbon blend (see the extracts of his book at http://www.pre-pro.com
McBrayer Whiskey, 20 gallons
Mattingly Whiskey, 20 gallons
Monticello (Rye), 5 gallons
Prune Juice, ½ gallon
(McBrayer and Mattingly were both straight bourbons. Also, the prune juice can be peach juice or any other fruited extract, he gives recipes for various fruit-based mixtures for this purpose).
One-half gallon out of 45.50 gallons is about 1% only - very small. All his fruit mixtures were spirit (GNS)- based, and the Red Stag is even better being bourbon itself - just a very sweet one. The Red Stag is, therefore, a perfect substitute for a GNS-based peach or other fruit juice. So is Southern Comfort. So too would be a sweet port or sherry.
If you try these combinations with that small a percentage, I believe the addition will not be noticeable, yet it will have served its purpose which is as a catalyst, essentially.
Of course, the final taste will be a function of the specific components. Maybe the perfect balance would be reached with a 2% addition or even 5%. It depends on each case and each person's taste. Still, it would be interesting to try something close to what Fleischman advises. I may do this tonight.