I've carried a badge for almost 22 years and as cops are recruited from the human race no two will react the same to a given situation.
MOST, but certainly not all don't get excited about long guns stored where access is limited. Handguns on the other hand are another ball game. I personally never get too worked up about a long gun, or a handgun unless its being pointed at me. I have been known to ask to look at something interesting, like a real Sturmgewehr 44 a guy was taking home from an auction.
Usually if you don't look like or act like a meth addict, a sovereign citizen, or you just crawled out of someone's window you'll get treated decently, but your mileage may vary. A little respect goes a long ways and usually is reciprocated.
Back to the OP, I would do an online search of each state and see how they classify black powder firearms. The NRA-ILA website would be my first stop.
Also, be sure and record the serial #, make, model, etc for all guns you are transporting. This sounds like a no-brainer, but probably 80% of the gun thefts I have worked the owner didn't have info for the gun to have it entered in the NCIC database. So many people think if they can describe it that'll work, but without a serial # it is real difficult to get entered.
This part is a sad commentary on the world we live in. If you have bumper stickers, window decals, or other identifying items on your car, in your car, person, or belongings; for example a NRA sticker, your NMLRA jacket you are so proud of, you USMC or Buckmark decal on your rear window, then you should call your insurance company now and start the claim.
Thieves know to look for these things that indicate the owner has/have/had a firearm about them. I personally know two guys who stopped at a diner in Dallas at night and came back to find their window shattered and guns taken from the truck, the only indicator was the NRA sticker on the rear window. Pretty brazen as there were cars everywhere and the lot was well lit. I would keep the rifle in my room, and transfer it to and from with as little fanfare as possible.
Personally I think the comments about your Miranda rights and having an attorney on speed dial are nonsense and hyped up by people who don't get away from their desktop often enough.
First, you are going to have to give the LEO a reason to stop you. Then the LEO will need reasonable suspicion or consent to search your car. Then probable cause is needed to arrest or seize property.
I tell everyone if you are a law abiding citizen you usually don't have much to worry about and not to get excited, or to act excited if you have contact with a LEO. Everyone gets nervous and that's expected; hell I got stopped a while back by a Trooper I didn't know and found myself stammering and fumbling my wallet. Try to remain calm and state what you're doing. To my knowledge it isn't illegal to cross a state line with a black powder rifle. If so then I'm in trouble myself.