Good question, as I had considered dropping back to 10 width, too. Yesterday, I spoke with one of the knowledgeable folk at Agwheelexrpess about exactly this possibility. Here is what I learned from him: Eleven inch wide, 16 inch diameter rims are no longer manufactured, so that is not an option. The gentleman at AWE informed me that a twelve inch width is actually preferable to 11 width, which are slightly undersized for a 13.6-16 tire. And, 12 X 16 diameter rims are currently being manufactured, so all one needs to do is make up the center disc to whatever is needed by the tractor and weld it in. Done.
But, I have a set of 11X16 wheels that have the wrong bolt circle and center hole diameter. Should I re-drill them and enlarge the center pilot hole? I could, and might still do that, but that entails bringing them to a machine shop to get it done right. They would need to be chucked into a lathe to assure the new pilot hole is concentric, and the new bolt holes would need to be indexed to correctly fit the hub of the tractor. This takes some time (translation $$$), and the new center pilot hole would intersect with the old lug bolt holes, definitely not an ideal solution.
Another option I considered was purchasing a pair of 1/4 thick reinforcing rings having the correct bolt circle and center pilot and welding them onto the wheels I have. This would entail reaming/cutting out the existing center pilot hole due to its being undersized, then welding the reinforcing ring over it with correct hole locations. But....finding a shop (I do not trust my own ability to get this done correctly) that can precisely position the reinforcing ring, then weld it into place exactly where it must be to prevent the wheel from being lopsided once mounted onto the tractor hub, probably not many near where I am located. Not to mention, this would be a costly procedure that would yield a final result far inferior to making a new flat disk wheel.
After kicking this one way or the other then back again.....for me the best solution, when considering cost and quality of end result, will be to go with the new flat disc wheel using a 12X16 rim. It will be strong, sized correctly, have powder coated paint and will look good, too. Like you, I have searched far and wide for a very long time to locate a set of wheels like those shown on the tractor photo you posted. Oh, I did find a set at a salvage yard whose name I will not post here, but they insisted on $750 for the pair plus shipping. That price is $200 more than having a custom set made that are arguably superior. So, they are not a contender.
Getting back to the 10X16 option you have found for a much lower price. If your tractor is 2WD instead of the critical 4WD model, its certainly an option that, depending on your tire, could be fine. 4WD is fussy about tire diameter, as the correct gear ratio needs to be maintained between rear and front differentials. Mounting a tire on a rim narrower than recommended will increase the overall tire height and rolling diameter, an outcome which might impact that critical rear/front gear ratio. If your tire is like the one shown in your photo, the narrower rim will cause the center to bulge outward a bit more than when using a wider rim, but not all that noticeable due to the tires profile. However, if you are going to mount a tire with a flat tread profile, you will not want the center to be bulging out due to the rim being narrower than recommended by the tire manufacturer. The rounded profile of the Farm Service Dia tire shown in your photo allows for some deviation from the recommended rim width. But, unless you have a set or can find a set of used, the FSD tires are no longer manufactured in 13.6-16 size. From my own research, a wide turf tire in that size is now limited to only one manufacturer, which might be Carlisle, but not for certain.
Well, thats the scenic tour of my own journey in making the conversion from ag wheels to turf wheels on the Bison S670D. Oh, here is one last thought, but this one about the front wheels. 6X14 wheels with 6X6 bolt circle and a 4 5/8 center pilot are common. And, they will fit onto the front of your S670D. BUT, they are oversized for a 6-14 Farm Service Dia tire, which is still currently available. Another BUT....if you want to simply mount a 185R70-14 auto tire on this 6-14 rim, the height of the 185R70-14 is identical in height to the 6-14 Farm Service Dia, which is 24.2 inches. This option is fairly easy to put together and costs far, far less. For a 2WD tractor that may only be used for mowing, it should be just fine. Not, however, a good choice if those front tires are going to be subjected to heavy weight as when a tractor is equipped with a front end loader. Then, heavier tires are of course preferred.
Vvm
