While it is true that the M1835, mountain howitzer's origin can be traced to the French mountain howitzer, the Model 1828, was not produced in any number until 1830. As such, it is very doubtful that one would find its way out to the St. Louis Arsenal, even by 1843.
As for the tube at the Nevada State Museum; it could be the Fremont howitzer as it is indeed from the same "batch"; received 16 May, 1837, and accepted by Army Inspector, George Talcott.
If the issued [to Frémont] howitzer was French, which could explain the handles, it would also explain why the Paulus Leeser / Charles Preuss drawing does not show the trunnions. The French M1828 had "quarter-hung" trunnions, that is that they were below the mid-line of the tube instead of at the mid-line as with U.S. cannons.
"One last thing; the "canister" for the mountain howitzer was filled with .69 caliber musket balls, but they were in a tinned tube with a tapered wood plug for the bottom, and a tinned disk for the top. There was no metal bottom. The howitzer used what was referred to as single-loading ammunition. That means that the powder charge was connected to a sabot which was connected to the shell, case, or canister. This "assembly" was loaded all at once, and not separately as naval cannon were loaded.
Here is what I have as the correspondence between Capt. Bell and George Talcott (Sr.)
Senate Document, 28th congress, First Session. Document Files, Iowa State Library.
Capt. Bell of the Arsenal to the Chief of Ordnance
St. Louis Arsenal, May 10, 1843
I transmit, herewith, the copy of an order from Colonel Kearny, commanding this military department, founded on a requisition of Lieutenant J.C. Fremont, of the Topographical Engineers, for certain ordnance stores, to be used by his party on an expedition to the Rocky Mountains, authorized by the government. The order appears to have been given by the Colonel only on the principle of the urgent necessity of the case, which as Lieutenant Fremont stated, would not admit of the delay necessary for reference to Washington. Under these circumstances, the order being preemptory, and the whole responsibility being assumed by the Commander of this Department, I felt it my duty, however reluctantly, rather than disobey a positive order, under these circumstances, to make the issue; and especially as it appeared to be a case of great urgency, from the statement of Lieutenant Fremont.
If in this matter I have erred, I hope the Colonel will perceive that it has been in consequence of being placed in a dilemma of some difficulty and that it has been from a want of anything but a respect of the order and regulations of my own department. I therefore respectfully ask of the Colonel his sanction to this issue, and his views as regards the propriety of my conduct in the case, which may be necessary for my future government.
I am, Sir, very respectfully, your obedient servant,
William H. Bell
Capt. Com'g Post.
Requisition for ordnance and ordnance stores, for an expedition into the Oregon Territory. Required May 8, 1843, mountain howitzer, 1; carriage complete with harness, 1; pistols, 4; pairs holsters,etc., 2; carbines, 33; kegs of rifle powder, 5; pounds of artillery ammunition, 500; tubes, filled, 200
J.C. Fremont, 2d Lieut. Topographical Engineers
Col. Kearny's Order:
Headquarters 3d Military Department Jefferson Barracks May 8, 1843
For the foregoing reasons, as given by Lieutenant Fremont, and as he is to leave tomorrow, and therefore has not time to hear from Washington, in reply to an application for arms and ammunition, Captain Bell, Ordnance Department, will issue on the foregoing requisition; the whole responsibility of which is assumed by myself,
Col. U.S. Dragoons
"A little info on the development of the U.S. M1835, see: http://www.currensnet.com/artlry/mhearly.html and http://www.currensnet.com/cwcongrs/Mountain_hwtzers/mh_b_dev.html "