Expect a lot of different opinions on this subject...
Here's my take.
The 50w engine oil is the equivalent to 90w gear oil. This gives good wear protection, especially if you're working the drive train hard in warm weather. Since the manual was written there have been improvements in additives. The GL4 90w gear oil is a popular one, has EP additives, better wear protection than engine oil.
The down side to using the heavy oil is slow lift performance in cold weather. If you're in a warm climate or don't use the tractor in cold weather, the heavy oil is fine.
For cold weather use, many like 10w30 motor oil. Your choice of 15w40 would be close enough. There is also a Universal Tractor oil at Tractor Supply that is in the same range.
So, a lot depends on how the tractor is used, the temperature range, and your personal preference. I don't think what you choose is as important as keeping it clean and dry. These are notorious for collecting water. It gets in around the shifter boots, the rear top link boot, and condensation. And, there is no hydraulic filter, so whatever is in the transmission gets run through the hydraulic system too!