If the problem is thick oil, synthetic won't get anywhere near as thick as conventional does....very likely enough that the breaker won't continue to trip.
You should up date your synthetic oil information.
Unless it's extremely cold, or extremely hot, conventional oil runs about the same viscosity, and about the same lubricity as conventional oil. There is some difference, but it's no longer meaningful.
You can see this for yourself, by comparing the specifications at "normal" temperatures of any synthetic, oil to any conventional oil, of the same weight. Even at 0F, there is no substantial difference, in either viscosity, or lubricity. That should settle it. However, many still refuse to accept that, even when it's right there in black and white.
I would put synthetic oil it, but mostly because no one wants to change the oil in their compressor. Mine has had the same oil in there forever.
The reason I said synthetic oil does not mitigate the effect of the cold motor is, the bearings in the motor do not know what kind of oil is in the compressor. They still have the same grease, and it's probably pretty thick in the winter, at start up.
There are other issues that could be in play, such as the wire size could be too small for the load, during a cold start up. That can cause a substantial increase in current draw. I would look into that. An amp probe will tell you right away if there is a problem there.
It may simply need to be put on a slow blow fuse, or a hy-mag breaker, which will dampen out the starting surge.
Building some sort of a heated enclosure, will extend the life of the motor, and compressor, for sure.