No one knows the exact number of .22/32 HFT's that were produced. As others have stated, they shared serial number blocks with the .32 hand ejectors so using a starting serial number and the highest known .22/32 HFT serial number will not get you there. Maybe someday if Roy or Don has time the records can be searched but it would be a long and arduous process.
According to my database containing over 2000 examples, I feel that there were 2 runs of 1,050 and one run of 490 accounting for close to 2600 whose left stock bottom received an assembly order number imprint. The first run which I researched in the factory records, thanks to the graciousness of Dr. Jinks, contains serial numbers 138,226 through 139,275. I have dates and destinations for almost all of this run except the dreaded few where the record was not readable. The dreaded "open on the books".
For the first run, 138,226-139,275 I have recorded imprint numbers starting at 1 and going to 1,018.
For the next run I have it recorded starting around 161,XXX to 165,954, I show a low imprint number of 1,094 on a Bekeart shipped gun shipped 5/18/1912 to a high of 2071 shipped in January of 1913 to Norvell Shapleigh Hardware in St. Louis, MO. The majority of the guns I have listed in this run went to Bekeart on either 5/18/1912 or 6/3/1912.
The last run of guns with imprints found on the left stock bottom are the 490 consecutively serial numbered guns that went to M.W. Robinson in 5 shipments on Jan 31, Feb 18, 21, 27 and Mar 19, 1914. These guns show a low imprint number of 2253 to a high of 2582 and start at 207,926 and end at 208,415.
The next serial numbers to appear in my database start at 220,110 and thereafter I never see another stock imprint number except a few fliers that I believe to be miss matched guns.
So my conclusions drawn from studying this model for the last 2 decades are that there were most likely 2 large runs of 1,050 in 1911 and then 1912/13 and a 490 gun run in early 1914.
This would represent 1050, 1050 and 490 or a total of 2590 guns. My recorded stock imprints run from 1 to 2582. Unfortunately, S&W did not maintain a record of these numbers or at least we have never found one. All of this information is based on observation.
So I believe that these stock imprints were halted after the M.W. Robinson shipments and when this model was put into regular factory production around mid 1914.
Certainly if anyone has an example outside of these parameters, I would love to hear about it.
If you own one and would like to share the information, (no owner info is recorded) I would love to add it to the collective knowledge.