I'm not aware of fork oil available in multi-viscosity. I have always purchased a fixed weight. The manual does call for 10W-20 but I always assumed that was just motor oil. Maybe there is, just not something I ever saw or considered. I have always used fixed weight fork oil... except in a pinch when I have used motor oil. Never did it on purpose.
In the past, many bikes called for ATF which also was 10W.
I'm not sure that I would change to a thicker oil unless you had a specific service in mind. On the street, with the many varying conditions, it may prove too thick.
There's another reason to consider staying with 10W that's not readily evident. That's the rear shock. ??? One thing about suspension tuning that's a standard is maintaining the front working in conjunction with the rear. If one end is acting much different from the other end, even if one is right, the package may feel worse than having both less than optimum, but equally so.
One thing that's nice is it's relatively easy and inexpensive to change fork oil. If you try one and it's not good, it's easy to change.
I would strongly consider the cartridge emulators. Especially for street riding. They really do make a difference. For those who don't understand their purpose, here goes.
The damper rods we have are fixed orifice. That means the damping rate, dictated by the ability of the fixed orifice (drilled hole)
to pass oil, are at best a compromise. The dampening is too soft at low speed fork travel, the small bumps, flowing the oil too freely, not dampening much at all. The passage is too large to have much effect on the low volume of the oil passing through them. Somewhere in the middle of that fork speed, caused by a little harsher bump, the restriction of the fixed hole is just right and has the perfect effect, perfect restriction and resistance to flow, perfect dampening rate. Then, when you hit a big bump and the fork needs to travel a large amount quickly, the hole is too small to pass the necessary volume of oil so is therefore too harsh. It's virtually hydraulically locked and unable to move fast enough. Very harsh! It's those errattic responses to varying conditions that the cartridge is designed to fix.
The cartridge is an assembly with a much smaller fixed orifice so it flows a smaller amount of oil at some restriction/pressure, dampening the small bumps perfectly. Then, as the bumps become harsher and a larger volume needs to flow, but still with some resistance to dampen the action, a spring loaded disc in the cartridge is hydraulically lifted by the increased fork oil pressure, affording the larger opening to allow the larger flow required, yet dampening according to how stiff the spring is to resist that lift. The spring in the cartridge is adjustable to vary that effect. It winds up affording the greater amount of dampening for the small bumps that the fixed hole couldn't do, accomodates the middle of the range as the fixed hole did, and then can really open up for the harshest of bumps, letting the fork move over them with the proper resistance, but not hydraulically bound.
If you think that through, does it become clear how that might be very desireable for the WIDE variety of conditions we meet on the highways?
Hope that helps.