I put a NOS Ford brand 3 spd. aux. in my '65 Ford 2000, straight 4 speed about 20 years ago. It was a million to one shot I even found one, new in the box, at a little country Ford dealer, we happened to be working by at the time.
To install, the front input shaft had to be removed, then the aux. trans. fit in that space. IIRC, once you fill that transmission, oil from the main transmission keeps the oil level up to snuff, coming through the front main shaft ball bearing, basically making it a common reservoir.
I remember there is a lip seal between the two, to supposedly seal the connection. I installed the OEM seal that was in the box, even though it was 30 y.o. at the time, yet seemed pliable. Sadly, a few weeks later I noticed a slight leak coming from the weep hole underneath.
I put it back in the shop, split the tractor again, and replaced that seal. A few weeks later, had the same thing. Both seals were properly installed, just figured it was a design flaw, and will be a leaker. I'd advise to check the oil level in your main transmission.
I'm not sure if that Ford transmission was designed on the Sherman trans. or not. This one has a Ford part number on the transmission case, and is still listed in the parts list for the '65 and newer 2000 and I believe 3000,
Schematic, Manuals, Specifications and Diagrams for Auxiliary transmission, over & under (accessory) | New Holland AG | MyCNHi US Store although a lot of the parts are N/A anymore.
I did keep the input shaft, and housing in case the transmission ever failed for some reason, and would just have to live with the straight 4 speed transmission, which is geared pretty fast for a lot of work. That's the reason I ended up with it anyway. The previous owner said it was too fast, for using a rotary cutter in heavy weeds. It was 35 years old, and only had around 1300 hours on it. At first, I thought maybe he just hadn't operated tractors much, but soon found out he was correct. That's when my search for the aux. transmission started. Thank goodness for the internet..!!
I'm also thinking if your getting a noise from the transmission, it could be a bearing failure, and could be repaired. Hopefully it would be a common bearing. If beyond that, find a good used input shaft/housing, and go with the straight transmission, although it may be quite a bit faster than what you're used to now. I'm thinking the over/under was at 10% on this one.