Okay.
How about some support for the distinction you draw between "ordnance" and "arms"? How do you determine that the first is not a proper subset of the second?
Can you provide anything prior to, say, 1850 that supports such a distinction? The "shot heard round the world" was fired in Massachusetts in April of 1775. The Regular Army of their own government was sent to confiscate what I would call "arms" in Concord that were in the possession of those opposed to that government's actions.
Each and every colonist who opposed that confiscation put their lives on the line to oppose what the government thought was a legitimate function of government. These colonists certainly acted as if they had a right to possess what the government was trying to confiscate.
Within the definitions maintained during the time period. To "bear" arms, as in "keep and bear" always meant 'able to be carried':
Often, the following, in this case excerpted from U.S. v. Emerson (see Part V [Second Amendment], C [Text], 1 [Substantive Guarantee], b [Bear Arms]), is used as an attempt to show bearing arms was synonymous with carrying:
Also revealing is a bill drafted by Thomas Jefferson and proposed to the Virginia legislature by James Madison (the author of the Second Amendment) on October 31, 1785, that would impose penalties upon those who violated hunting laws if they "shall bear a gun out of his [the violator's] inclosed ground, unless whilst performing military duty."
This may be limiting, but within the rationale of the day. So, in order to fulfill the definition of 'bear' a weapon needed to be able to be carried, of which, cannon cannot. Further, the dictionary of the day defined ordnance as :
Full Definition of ORDNANCE
1
a: military supplies including weapons, ammunition, combat vehicles, and maintenance tools and equipment
b: a service of the army charged with the procuring, distributing, and safekeeping of ordnance
2
: cannon, artillery
A web site that I frequent has compiled a rather exhaustive list of support for the 2dA and the RKBA: Guncite on 2d A