I don't know what the rotaional rate is but I know that on slower bows you can see the fletching turn on its flight to the target.

Just thinking out loud...

It might be possible to get a rough idea from your foam target. If we knew the (1)velocity at impact (2) the depth the arrow penetrated) and (3) the number of turns when you pull the arrow out (assuming it follows the same path in I think we could get a pretty good estimation.

Another thought is that it can not exceed the total energy loss after the initial launch. As the rotational energy comes from the energy of the forward motion, then if you have 60 ft/lbs at launch and 55 when you hit the target then the rotaional energy must be less than 5 ft/lbs. If for example we then measured 4 ft/lbs rotational from the "walks with a gimp foam target experiment" we could conclude that 1 ft/lb of energy had been converted into other losses like friction and heat.

And another way at the answer might be to measure the ke of the helical fletched arrow at say 30 yards and then a straight fletched arrow of the same type at 30 yards. Assuming the straight fletch flys without rotating and the helical rotating then the differece measured in ke should be the answer. I think this would actually be more accurate than trying to measure the turns in your foam target. It seems to me that somebody somewhere must have done this experiment. Come to think of it anybody have access to a good arrow ballistic calculator? My bet is you could run these 2 conditions and anwer walks with a gimps question.