IBM was issued only one serial number block: 3,651,520-4,009,999. So your rifle was one of the first 25,000 of the grand total 346,500 IBM made between August 1943 and May 1944 at the IBM plant in Poughkeepsie, NY. They were the last to receive an M1 Carbine contract from U.S. Army Ordnance, on February 16, 1943.
IBM Manufacturing History:
The barrel date 9/43 would be correct for an IBM in the 3,670,000 range.
One of the things difficult to explain and understand are all the changes that were made and things specific to one manufacturer that the others may not have done. Like the P on the barrel, absent on some barrels. The p proof mark isn't on yours because it has an equivalent, the flaming ordnance bomb. Some IBM barrels have the P, some have the Ordnance bomb. Some were dated, some were not.
U.S. Ordnance assigned each manufacturer and their subcontractor a 1-4 letter code to identify who made which part. These were assigned part by part, not company by company. so some companies used one mark on a sear and another mark on the trigger, yet they were the same company. Not all parts were marked post WWII. Small parts like springs and pins were not marked. Generally, the location of the mark, the font, and the size vary depending on the contractor or subcontractor.
Post War Rebuild History:
In a nutshell, if the carbine was returned to the USA it went through this inspect/rebuild process. Who did the inspect/rebuild on yours is indicated by the U with dots on either side, on the left side of the stock. Underwood was contracted to operate an inspect/rebuild operation about 1951. That U and dots on your rifle means Underwood.
As part of the inspect rebuild process the carbines were totally disassembled, each part inspected, then totally rebuilt from the parts bins. The parts that came off a carbine didn't stay with the carbine. All were interchangeable so they separated them by part, not by who made it or what carbine it was on when it arrived.
Certain parts were mandatory replacement parts. The barrel band with bayonet lug, the rotary safety, the mag catch with the big M (holds 30 round mags better than those without the big M), the adjustable rear sight. Yours has all these upgrades, meaning it's consistent with a carbine that went thru the Ordnance inspect/rebuild process.
Which brings me to the stock. The stock was manufactured by Trimble Nursery in Rochester, NY(TN in the slingwell. Funny thing is, Trimble made cribs and other wooden childrens items before the war.) for carbines manufactured by National Postal Meter (NPM with Ordnance inspectors initials and proof mark on right side of stock). It may have been placed on your carbine at the end of the rebuild process, or by whoever used the carbine later.
The 1 and 0 on the bottom of the stock grip was what is referred to as a rack mark. As is the serial number in the left side of the stock. Whoever used the carbine stored it upright in racks. The numbers allowed them to distinguish one carbine from another while in the rack. Usually if the rack mark is on the left side, the rack held the carbines at a slight angle exposing the left side of the stock. If the rack held the carbines upright, the rack mark on the handgrip would be used. The SO or whatever it is on the right side of the stock was put there by someone who used it, for whatever reason they had.
The question is, who used it after it was rebuilt?
I might have an answer for you. Look close at the barrel between the stock and front sight. See if you can find a marking with letters like C.A.I. over Georgia, VT or NWM CO over SAC CA. These are importer markings, placed there by the company that bought the carbine and brought it back to the USA. This marking has been mandatory since 1968. Yours probably has the C.A.I. markings. Before I go into what they mean, let's see if they are present. Also, let me know if the marking is stamped or engraved or etched. Those engraved are like the old dot matrix printer with the letters made up of a series of dots. This info helps me date when it was brought back.
I suspect who used your carbine was Israel. They are the only country I'm aware of that used the serial number in that location on the left side of the stock, with that size and type font. Two companies imported these, Century Arms and New Helvetica Marketing Corp (Old Sacramento Armory). Assuming someone didn't swap the stock out after it came back. I don't think that's the case, looking at the pictures.
What you Have:
A genuine U.S. Ordnance contracted M1 Carbine manufactured by IBM in late 1943, that is historically correct for where it's been and what it was used for. Collectors tend to prefer the "all original" markings on their carbines. That's what I call the Golden Fleece. These were made as war babies, not for someone's collection. When I see an "all correct" carbine I'm very suspecicious that someone somewhere reconstructed it into what they believed to be all correct. Long story, but these guns were made for war during wartime, reconditioned, went to war again, reconditioned, then provided as military assistance to other countries. Over half the carbines made were given or sold to other countries 1941-1983 and maybe even later.
Have a look at my page of records extracted from the National Archives that show who got what and when...look at Israel:
Foreign Military Assistance
This is a word that can have different meanings to different people. It infers the carbine or it's parts were counterfeited by someone and built into something they could sell as an IBM. If something gets "counterfeited", it's usually the markings on the parts. Markings get removed and replace them with markings that are much more rare and valuable.
This isn't the case with what I can see of your carbine. If someone wanted to up the value they wouldn't put those parts on it, they'd use parts from an earlier time period. I don't need to know the markings for this evaluation, the parts speak for themselves.
Different people are interested in different things, so value is what the majority usually will pay for it. From what I have seen of yours, it's worth ~$800. Maybe a few dollars less, maybe a few more, depending on the insides. I'm assuming there is an import mark, which devalues a carbine but at the same time helps reconstruct it's history.
I'm a bit different than most collectors. First, I'm not a collector of anything. My interest is history, and the M1 Carbines are my area of interest. I'd much rather have a carbine that I preserve it's overall history than one someone reconstructed into eye candy. I own 15 GI carbines that are part of a historical display I plan on donating to a museum. I have a separate as a shooter I built from surplus GI parts onto a receiver made in the mid 1990's by Springfield. I have a reference library of about 25 receivers and barrels from various different manufacturers. Some are broken. All are good reference material.
Hope this is what you were looking for.