Almost nobody knows of the Harwood Hornet.  I certainly didn't.  Only a chance comment by a friend on another forum gave me a clue, and Bent_Ramrod's copious memory for old magazine articles provided details.   

Here's the two Hornets, side by side.   

Below 2000, they would have to be New Ideals, the precursor to the 44, yes?   By the catalogs, the 44 designation doesn't start until 1896 when Page took over the company.

107 / 108 / 109 / 110 in ascending order of wood quality and sights.  That one's going to be a project.     I wonder if anyone at a certain agency is paying attention to how they are described and traded.  (shhhhhhhh!)   

That's an interesting tidbit - that they increased the diameter of the screws.   Mine are also .228" shank diameter.

A goodly number of purposed-built schuetzen rifles were made on the 44 action, 1896 to 1903 approx., and in .32-40  and .38-55, too.   I would dearly love to survey a few of those to determine features such as pivot diameters, lugged hammer (yes or no), fit to the shoulders, etc.  We know that schuetzen shooters thought nothing of firing thousands of rounds a year in practice, yet these old 44 style actions must have held up, or Stevens would never have sold so many. 

Another question that nags me is how they finished those shoulders.  In my 108 they seem to have a curve to them, which argues for some sort of rotary broach that pivoted on the breechblock screw.  The only way I can think of that would create a radius to match the swing of the breechblock.   

My receiver is gone grey, but by squinting real hard I can convince myself that it was the "pinto" pattern so characteristic of Winchester, and not the "ripple" pattern.  

Took the buttplate off.  Had not done that before.  On the wood are a few characters in what looks like felt-tip pen.  Too faint to be really legible.  D ? I ?. Second character might be an R, 4th character might be N or M.   There are more characters on a line below that which I can't make sense of at all.   The brass plate is crisply stamped with a number 1, and in a different location with the last 2 digits of my serial number.    The forend is also stamped with those two digits.   

I guess if we're simply talking a model designation, then yes the 44 would be a later model. But the receivers really are so similar that I've always lumped them all into the "44" type guns. It's not correct from a true collector standpoint.
Some of those larger caliber 44's are still around and still very tight. But not all of them held up, and many are found extremely loose in calibers like .38-55, .32-40, and the larger pistol calibers like .44-40 and .38-40 too. I've owned a number of them in the larger calibers and found about half of them had worn the pins out.
There was also a design change in the receivers from early 44's to later. The early ones have a very hard internal corner shape at the vertical transition to the receiver top. Later models have that corner rounded to avoid cracking that some early receivers exhibited. I would guess Stevens must have had some issue way back then, or they wouldn't have changed that design. You can see in this picture my 44 in .32-20 has a gentle inside curve to the transition:
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Here's my 107.  Somebody "customized" it for fair, but it seems to have been well taken care of for all that.  The barrel is lighter than any Stevens single shot I've seen, short of 044-1/2's and Ladies Models.  It has the J. Stevens A & T Co markings on the barrel, and the barrel has the same number as the receiver.  Caliber is .32-35.  The frame has the right angle, and the barrel protrudes deeply enough so you can see a little of the extractor.

Blew my theory up all by myself last night, with a stroll through Gunbroker.   There's a .32-40 on offer right now with the 6 o'clock extractor.    GunBroker.com Item 407393445

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Another question that nags me is how they finished those shoulders.  In my 108 they seem to have a curve to them, which argues for some sort of rotary broach that pivoted on the breechblock screw.  The only way I can think of that would create a radius to match the swing of the breechblock.  
 
How this can be done, mount the reciever on a face plate with the breechblock pin hole centered on the spindle axis. The reciever needs to oscillate back and forth about 40 degrees on a 44. Looks to me like a verticle tool slide would be needed and the reciever oriented with the tang up. To do the cut rock the reciever back and forth by hand and advance the tool into the cut. This is basically a shaper operation. I've not done this on a 44 but do have a reciever that is rusted badly in that area and "someday" plan to clean it up and make an oversize breechblock. Hope that explaination was followable. 
kootne