Although the stock in the photo of the gun above may be original to the gun, all the early straight gripped 444's I've ever seen have a Monte Carlo combed stock with Marlin marked white-line rubber recoil pad as seen on the gun in the pic below (gun at right in photo). But there are also other factory 444's with straight gripped stocks; special limited runs with 18" barrels, and some examples even have ported barrels. Unfortunately, I don't recall the model designations for these 444's; but understand they are a hoot to shoot.
All early original straight gripped 444's I've seen featured a Lyman fold-down rear site; but as I don't have any period catalogs handy, that feature could have been changed to the ramp type sight later in production. According to what I can remember from my research, 1972 was the final production year of the early model 444T; and was in fact a transition year, as one will also find examples of the pistol grip 22" barreled 444S Model from 1972 ("S" designating Sporter, as opposed to the "T" designation for Texan).
The gun in the photo below is a 1969 vintage 444 with the Lyman rear sight. And one final note, if my old memory serves correctly, 1968 was the year that Marlin began stamping serial numbers onto the top tang as opposed to the lower tang. At that point it became very simple to date a Marlin lever, as the first two digits would be the year of production.
So in 1968 each lever gun serial number would begin with the numbers "68"; and Marlin used this revised numbering system thru 1972. Then in 1973, and again in my old memory is correct, the numbering system was changed again so that the first two digits of the serial number must be subtracted from 100 to determine production year; which would mean (if memory is correct) that lever gun serial numbers for 1973 production began with the number "27".
Marlins can be confusing at times, but all this confusion just serves to make collecting more fun and interesting.