You say that besides three infantry regiments, soldiers had to be in the new uniform by fall of '33. What regiments are you talking about? I've heard that the 7th Infantry wore chakos until as late as 1837 until drawing for the folding cap.
There is much confusion afoot, I fear, mixed with "Reenactorisms" or make believe claims to excuse anachronism.
The confusion comes, where some in the 20th Century confuse the "cap" for the "chakos" or "forage cap."
The Cap was what 20th Century people started calling a "shako." The US Army in the 19th Century didn't call them shakos. They just called them "caps."
Caps: (1821 of leather at left, 1832 of wool felt at right):
The "forage cap" differed because it was for fatigue or forage wear. It was generally for wear with the fatigue dress of the soldiers.
"Forage caps": (1821, of cloth at left, and 1832, of light leather (imitation Morocco) at right):
Then there's the "chakos" of 1825-33; unique in that it had a name.
The "chakos" of 1825-32 was distinctly named, evidently, because it was a part of the uniform, worn when the cap was not, as in off-parade or duty, so was not a "forage cap" per se. But it was initially ordered to be worn
in lieu of a forage cap in the fatigue dress too (see 1825 regulations).
The regulations were amended, upon adoption on March 1, 1825, to reflect that the chakos was to be
the forage cap...
In the proceedings of the military board of February, 1832, regarding army clothing, it was noted a number of line officers had specifically requested the "chakos" be eliminated. They were shabby and wearing a wet woolen rag on the men's heads in cold weather etc. was no good, and consequently it was classed as "unfit for service." So the Army subsequently adopted the water-proof "forage cap" of light leather in 1832/1833, "unbecoming" as some considered it. The new uniform of 1832 also included the new "cap" too, of felt instead of leather. So after 1832 there was a new cap
and a new forage cap.
So we come to the Troops actually receiving this new uniform and clothing:
In February, 1833 it was directed by Army General orders that all old pattern (1821-32) uniform clothing on hand or stored in depots,
except caps, were to be issued "as far as it will serve" to the 1st, 3rd, and 7th Regiments of Infantry, then posted in the northwest. So it appears these excepted regiments were to receive the new uniform cap, and that the old pattern cap was to be immediately replaced that year among them.
[HQ, Army, Adjutant General's Office, Orders #10, paras. I-III, Feb. 9, 1833,: Recs. Of the War Dept. AGO, Bk. 10.]
By April 1834 the collection of old pattern clothing had been turned over to the quartermaster's department proved so large it was deemed necessary not to sell it, but to continue issuing it to troops of the aforementioned three infantry regiments. [Military & Naval Magazine, III, 3, May, 1834.] The entire collection of old pattern caps (1821) were, however, in July, 1834 turned over to the Marine Corps (which continued to wear them until 1859).
It was at the same time noted that all other troops were to receive the complete new uniform certainly in the fall of 1833. Thereafter, only the old pattern gray jackets and gray greatcoats were allowed to be employed officially, where necessary; and the new pattern ones gradually introduced by regimental requisitions, etc. in the next year, etc.
So, the question remains relative to the "chakos:" was is yet worn by the the 1st, 3rd, and 7th Infantry regiments were still receiving the old pattern clothing "except caps" after the fall of 1833? The answer is evidently no.
The 7th Infantry, for example, had already drawn the the new leather forage caps in April, 1833, several months before the fall 1833 general issue of new pattern clothing... (Kloster and Howell, US Army Headgear..., p. 36.):
So it would appear that the infantry regiments in the northwest, by the close of 1833 were outfitted with the new caps, the new forage caps too, but their other clothing was of the 1821 pattern until that was worn out in service.
There is no evidence the Chakos was worn by any US troops after 1833, either in lieu of the new pattern cap or the new pattern forage cap. Recall the previous year, it was recorded as entirely unfit for wear in the service.
Some of confusion relative to modern claims the chakos forage cap was yet worn to 1837, might be, because the 1825 edition of Army General Regulations, which mentions them in its text as the forage cap, were only replaced by a new edition of the general regulations, effective as of January, 1, 1837...
But the uniform of the army had been changed in the interim, and some scholarly sorts might not have been aware of that fact.
The confusion too comes from an unfortunate comment in Kloster and Howell's excellent book on US Army headgear. In the chapter on the 1832 forage cap, they state:
the document noted is General Order no. 53, of July, 1834:
Referring to that document shows that it does not state what Kloster and Howell suggest in their text. As mentioned, it just says the old pattern Caps were collected and turned over to the Marine Corps, so they could not be worn with the old pattern clothing distributed to those infantry regiments. And of course, as even they state, the 7th Regiment at least had been provided the new leather forage caps over a year prior to that general order; so the general order in question has nothing to do with authorizing the continued wear of the chakos, which had already been replaced over a year before.
Among reenactors, I have in the past talked to some that wear the chakos for 1830s interpretations. Even if pointed out the regiments wearing the old pattern clothing otherwise, were provided with the new forage caps in the spring of 1833, they just say something like "the leather (1833) forage cap is ugly, etc. etc. So they wear them as a "reenactorism."
In 1839, the Army adopted a new pattern forage cap, of particular blue cloth treated so as to be somewhat waterproof. In general use by 1841-42.