With a spool no special additive is needed... whale oil or otherwise. For your intended use just about any gear lube - like 80W90 - should work OK.
Sustained high speed running and/or high temps would favor higher viscosity synthetic to take the heat but not an issue on the drag strip. xxW-140.
The last .01 second ET in the quarter mile might favor favor a lighter synthetic like 75W90.
Personally I would probably put 80W-90 in it.
I used Valvoline or Pennzoil 85-90 Wt. petroleum based non synthetic gear oil, CRS now
, in my old pump gas Duster with a strange 35 spline spool in both the 8 3/4 and the Dana 60 after I bent the stock type 8 3/4 housing up bad enough to pull the welds off of the ladder bar brackets on the passenger side during a run, luckily that happened on the starting line and not later
That car ran mid to low tens through the exhaust on Oregon 91 octane pump swill weighing 3450 lbs. with me in it, no problems on the gear lube ever
