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If you feel a real need to keep the weapons and ammunition completely separate, perhaps you could ship the ammunition to yourself.

Bring the weapons in the trunk, with some type of trigger lock on each, you could even ship the keys to the locks back to yourself so that you would not be able to lock and load.

I don't know that I would be particularly nervous about being pulled over. Obey the traffic laws, don't do anything stupid.

Your vehicle can not be searched without probable cause or your permission. When asked for permission to search, the answer is always "no". Doesn't matter how clean you are, the answer is always "no". If told they will bring a dog over to sniff that is their prerogative. If they say they will get a warrant, they are welcome to go ahead and do so. With either the dog or warrant, they may be running a bluff to get you to "give" your consent to search. Does not matter, the answer to a voluntary search is always "no".

IANAL