I'm assuming that since you're strapped for space that you must be riding double? Search for some extra luggage (T-Bags, Saddleman, etc.).
All I can say is that I learned many years ago to not leave home without my leather jacket (and hopefully a removable liner).
I always carry three pairs of leather gloves (light, med, heavy) and a pair of rain mittens for the heavy gloves, vest, leather neck dickie, leather pants, heavy rain suit and gators that fits over leather jacket, pants and boots in my saddlebags, in addition to my tools.

The weather out WEST changes both rapidly and dramatically and you'd do well to plan your travels from early July to perhaps mid-August, especially in the higher elevations.

 

Bring the leather jacket, was there last year during the rally it was 100 degrees on Tuesday afternoon when I got to Red Lodge MT. The next morning at the top of the pass it was snowing and in the 30's. Glad I travel with my heated liner that morning, by the end of the day I was back in Hill City in a t-shirt.

 

My first time over the pass it was cool on the way up the pass. We got to the top stopped and put on some more gear, sweatshirt. It started raining right as we pulled out to go down the other side. I was last in line and had a stack of cars behind me pushing me to go faster, but I couldn't see far enough to find a spot to pull over. I was a nervous son of a gun for a while, lets say that was not a fun ride. My second trip over, weather was perfect, cool, but no rain. Like the Scouts say: Be prepared.

 

Yea the possible strapped for space problem comes in when the wife tells me she might fly out and do Yellowstone, then fly back. Her taking up the passenger seat, extra sleeping bag, mattress, clothes, leather, rain gear...........

 

I cant believe you'r even riding up to Sturgis without your leather jacket to begin with. Lots of ground to cover from Miss to South Dakota and plenty of crazy weather. Chaps you can live without but my leather goes with the bike.

 

Road the Beartooth Highway in 2010. Temps at Red Lodge were in the 90s. At the higher elevations there was snow. Definitely take a leather jacket or a heated vest.

 

I prefer to bring a heated liner just in case when going into elevation. Takes up less room. A heated vest would be even better. I might add one to the closet. Don't forget heavy or heated gloves.

 

I still think that light jacket and rain gear will suffice if it gets unusually cold. You will not be on Beartooth all day and you will not be running 80 mph. If you keep your hands and head warm and dry, you will be comfortable.