There's a partition, wall, between the transmission and final drive, but oil flows through the big ball bearing that supports the back end of the lower transmission shaft. The big bull gears pick up oil from the lower part of the rear section and throw it through a space between the partitian and top cover or operator's platform. there's channels cast into the top sides of the transmisdion that lets the oil flow up to the front of the transmission and oils the front upper shaft and the pilot bearing between that shaft and the sliding gear shaft that also has the pinion for the final drive. The pto shaft pilots on the extended back end of the lower transmission shaft.
There's sectioned drawings of an H and M, might be Super M, should be on internet somewhere, I probably have a dozen copies in various books, but shows the parts of the transmission clearly, save countless hours of questions and typing long posts.
You should order a parts book and service manual from Binder Books, lots of good pictures and exploded viewd of your 350 Utility.