A number of interesting comments and observations have been received as follows:
From Joe in NH:
Generally I thought the Thayer & Houghton improvement of 1853 was the use of a separate feed rod which afforded flexibility to the operator in choosing feed - an operative improvement as each cut using high carbon steel tools on carbon steel was a machining adventure! The advantage of the separate feed with the feed pulley to the front (which forced for a time the lead screw to the rear) was that a wooden stick could be used to "jump" the feed belt from one feed ratio to another possibly even with the lathe in motion. Another advantage that MAY have been promoted by T&H was the use of a "rise & fall" type arrangement for the toolpost - this for the same reason of tool adjustment while on the fly. But on this I am not as certain.
Well, it was a rustic time operationally in many ways.
Not having this feed rod, I might opine that this lathe is probably earlier than 1853 and given the simplicity in comparison likely a developmental predecessor to the Ames Lathe seen elsewhere on your site. This one a "one at a time" production effort while the later Ames lathe was likely built in "lots," and marketed in greater quantity to a wider mass market. Although a feed rod might have been seen as a redundancy to a lathe used primarily "manually" - that is except for precision threading operations for which it excelled.
This (these) are the lathes that were used to make taps and dies, the cutting edge of this lathe production being manually "relieved" using a file or grinder. By the 1890s manufacture of taps & dies had been pretty much automated and became mass produced, and relief was built in on initial machining/grinding by "relieving lathes."
The square tailstock quill of this pattern lathe was later abandoned even by Ames. It's application was most likely before the Civil War. It did involve persnickityness to manufacture and didn't afford that much of a precision advantage.
Note also that the Stark Lathe pattern of the early 1860s largely took over the work of these square spindle boxed tailstock lathes, and by 1870s had ended their tenure. The earlier lathes had become "old fashioned" in market estimation. The adaptability of the Stark Pattern to "accessories" (including relieving tools), and the willingness of the Stark type manufacturers to produce them, may have contributed to this earlier lathe's market demise.
And I wonder to a familial connection between Hannibal and Joseph Houghton. The Internet may reveal more on this. As T&H merged and morphed into New York Steam Engine Co. and only slightly later into New Haven Manufacturing, it is apparent that Hannibal Houghton was comfortable moving around. Even by the 1870s, it was an era where one could board a train in Worcester in the early morning, and be in New Haven for lunch - and in Newark, NJ by mid afternoon.
If the Joseph Houghton (JH) is dated after 1850 then presumably it pushes the Chicopee lathe (the top pictures on that page) date back towards 1860 (the latter part of your estimate). Certainly the Chicopee lathe is very similar to the JH in many ways and could be a (perhaps competitive) development of it. The carriage design is strikingly similar (the half-nut hang slightly below the edge on both machines) The reversing gear used on the Ames looks like it was a simple mod to a JH apron (the through-hole of the JH used to support the end of the geared handle on the Ames)
Interesting how the JH's half-nut are operated by a tiny square key - suggesting they were operated in a different manner to conventional threading - I suspect they didn't thread up to a shoulder very often.
From Joe in NH:
Interesting that little square, obviously for use of a tool to "set" the half nuts.
But this is explained in that the half nuts, once set, would be left "on" from the first cut of a thread until the last. On reaching a shoulder, the lathe would be stopped using the overhead countershaft, possibly wound by hand up into the corner of the shoulder by manually pulling on the belt, and only then while the lathe stopped is the tool withdrawn. Then lathe would then be "backed" using the countershaft and without undoing the half nuts back to clear on the cut. The tool would then be reset, and given another quarter-half turn to advance the cut, and the lathe started again.
My circa 1860-ish Shepard, Lathe & Co. lathe has no half nuts. Rather a "dog leg" connection between a full nut (no half) on the leadscrew and the carriage. This dogleg is "set", bolted in place, and left connecting the carriage to the lead screw nut for the entire time a threading operation is performed.
A different, less time intensive time. In fact lathe countershafts were frequently made "two speed" with the slower speed being for threading, and the quicker speed for drawing the tool back to the start. This done by different sizes of driving pulleys on the main line shaft and connecting to the lathe counter by the usual uncrossed/crossed belts. .