The relevant statute is RSA 159:4
159:4 Carrying Without License. – No person shall carry a loaded pistol or revolver in any vehicle or concealed upon his person, except in his dwelling, house or place of business, without a valid license therefor as hereinafter provided. A loaded pistol or revolver shall include any pistol or revolver with a magazine, cylinder, chamber or clip in which there are loaded cartridges. Whoever violates the provisions of this section shall, for the first such offense, be guilty of a misdemeanor. For the second and for each subsequent violation of the provisions of this section, such person shall be guilty of a class B felony, provided such second or subsequent violation has occurred within 7 years of the previous conviction.
This would appear to suggest that what you say about Ohio's way might be the way up here. I would recommend contacting the NH Attorney General's office for final clarification, before you make your trip.
My prediction is they will affirm the definition as it appears in the statute. Your worst case scenario is keeping cartridges boxed with a speed-loader while you are inside your vehicle. Unloading your mag when you re-enter the vehicle, and clearing any round that is chambered.
You can carry openly or concealed with an empty pistol (including one with an empty mag inserted). This "poker carry" is fully legal without having a license under the above statute, both inside and outside of your vehicle.
I linked the Attorney General's office contact information in the thread in this NH forum about rifle laws. Please let us all know what the result is.