Narrow skins for wide skis?

I'm not a skilled skinner so I'm just asking here. But has anyone toyed with buying straight, stock skins that are substantially narrower than the ski, even under foot? Because with wide skis and skins cut to fit I feel like I'm getting plenty of uphill grip but horrible traversing edge control.

My skis are 130 at the tips and 108 underfoot. I bought backcountry.com skins and used the factory slicer to contour them and they appear to be perfect. But I'm not getting anywhere the side grip I need on any side slope that isn't deep powder.

On my skis with less sidecut I often use straight skins several mm narrower than the waist and just long enough for the tail fix to work--helps glide & tracking, reduces weight and bulk of skins, and is fine for climbing the way I like to climb--aesthetic switchbacks utilizing contours and avoiding up and down etc.  I even did the same on one pair of my powder skis.

However, on skis that I expect I will use on steep slopes and sidehills I use wall-to-wall skis that just leave the edges fully exposed.

I don't believe the problems you are having are due to the skins.  Proper traversing technique on steep firm slopes often includes sliding the ski forward thru the snow with the shovels setting a groove (a Wildsnow.com tip), depending on the steepness the skin can help with grip. 

But wide skis are more difficult to traverse with under those conditions.  Narrow skis usually have better grip because a greater proportion of the downward pressure goes to the inside edge and there is less of lever effect to the outside as with wide skis.  That is why downhill racers often use narrower skis as well as tall stiff boots.  Ski mountaineering skis generally are narrower than powder skis for that reason as well.

One thing that can help is to make sure your cuffs (all the boot) is snug enough to let you use the edges by inhibiting the outside ski edge dropping well below the inside edge. 

Finally, tuning your edges (increasing side angle to 2 degrees, sharpening, and polishing).

Try to traverse a steeper, firm snow slope without skins but with your boots loose--there will be lots of slippage and you have to concentrate to put enough downward pressure to have the edges bite and hold; traversing with snug boots (including making turns down) is not a problem.

I'm not a skilled skinner so I'm just asking here.  But has anyone toyed with buying straight, stock skins that are substantially narrower than the ski, even under foot?  Because with wide skis and skins cut to fit I feel like I'm getting plenty of uphill grip but horrible traversing edge control. 

My skis are 130 at the tips and 108 underfoot.  I bought backcountry.com skins and used the factory slicer to contour them and they appear to be perfect.  But I'm not getting anywhere the side grip I need on any side slope that isn't deep powder. 

For holding an edge while climbing, you'll want wall-to-wall skins. Skinny skins do have their place, but generally that place is for flat skinning, like long road approaches.

If you're skiing late-ish spring conditions on skis that are 108mm underfoot, I'd say that's your problem. I'm an incorrigible old-schooler, but I don't use skis wider than about 80mm underfoot (actually 70mm is more typical) in late-ish spring (which for this year, means now). When I use fatter skis in spring, I find lateral climbing very uncomfortable, as the wide skis are constantly trying to turn my ankles to the outside.

If you want to stick with the wider skis, try adding ski crampons.

If you think wide skis make sidehilling difficult you should try splitboarding

There's a reason why most of us two-up, one-down plankers dislike traverses...

Ski crampons avoid much of the hassles of not having wall-to-wall carpet covering the entire ski base.   With them it's no longer necessary to edge the ski on firmer snow to keep from sliding sideways.   The ski can lay flat on the slope and get maximum forward traction from the skins.   

We use ski crampons in spring time. Recently, I put on the crampons" before" it started to get steep. I learned years ago that when it gets steep you have the problem of putting on the crampons, when you realize that slipping is not a "happy" event. Stop before you are going up some steeper terrain. The crampons will not affect your climbing time. You may be the "first person" setting a track for your friends.