Couple of thoughts. 10w40 is really not the greatest choice. 10w40 tends to degrade to a 30w oil somewhat quickly. It is extremely prone to shearing. That is why it really is not very popular any more. It works, but one has to really track how it is holding up to confirm if it will do the job properly for the interval they run it. That requires several used oil samples. One of the most stable oils is 10w30. Some top end synthetic 10w30 oils are actually a straight 30 and are very stout, but they meet the cold flow rate to qualify as a 10w30. 5w30, given todays improved viscosity modifiers would work fine in many applications. If one is bound and determined to use a 40w oil, one of the modern full synthetic 5w40 oils would be the best option.
Synthetic does not keep an engine cleaner than a conventional oil. it is the additive package in the motor oil that actually is responsible for keeping engine internals clean. And the add pack makes up 20% of any motor oil, synthetic or conventional. It is true that a synthetic generally will have a lower NOACK, or burn off rate than a conventional. But that tends to affect oil viscosity over time. Synthetics tend to be a little more shear stable and hold up under severe conditions better. And, of course, synthetics tend to flow better in extreme cold. But for most folks, it would really be a stretch to prove a synthetic is doing them something that a good conventional could not also do. I tend to straddle the fence and use synthetic blends. Best of both worlds and virtually the same cost as a conventional alone.
Personally, I have been a fan of 10w30 oils for quite some time in just about everything I own. From my John Deere zero turn mower on up thru the 12.7L Detroit Diesel engine in my semi truck. But, if one is going to be dealing with some very cold starts in the morning, a 5w30 would probably be a better choice. I do use a 5w30 in one of my engines, but that is primarily because it only gets changed once a year and that oil has to do a good job, both winter and summer. My personal vehicles are garaged (heated in winter), so using a 10w30 in them is of little issue. Even when the temps outside are down into double digits below zero, my personal vehicles are in 50F temps in the garage. And neither of them have to sit all day in the cold at some work location. Advantages of running my own business and using business vehicles.