The Staples near me has a number of "Binder Gear" pockets on the clearance rack for $1.80. The system consists of a zipper pocket with an elastic loop on the back, and a piece of elastic with clips on each end and velcro in the middle. The pouch slips over the elastic and is held in place by velcro.
The clips on the elastic strap are designed to hook onto the top and bottom of a standard loose-leaf binder -- but I thought they might work just as well on a car visor. The pouch is a nice size for fitting a small meter and lancing device... or a roll or two of lifesavers or glucose tabs.
While the clip depth is too shallow to stay on the visor in the longer dimension, if you twist the elastic once around, the two clips can interlock together.
In this configuration, the elastic band can be fit over the short dimension of the visor, making your spare meter (or your emergency glucose tabs) readily available.
As an option, you can mount the band alone (or sew up your own elastic band, or use another sturdy band) and the Velcro-attached belt loop of your existing meter case.
On the plus side, this allows you to easily mount and dismount the same meter you are travelling with. I don't recommend this type of mount, though: the weight of the case may cause the Velcro to open, and the meter case to drop down on you, on a fast turn or sudden stop.
Another option is to run the elastic through the elastic band on the spine of your One Touch meter case.
This is very difficult to do with the Binder Gear elastic, as the plastic clips are a very tight fit through the UltraMini case's spine. Again, this is not a recommended mount, as the case will be dangling down from the visor and could impede your vision.
On the other hand, if you can set an elastic through that spine, you can easily carry the meter around your wrist.
Another option is to use the elastic alone, and just shove the meter case through the elastic. (You can also use the pouch to store lifesavers on the flip side.)
A completely separate but related item: if your vehicle has a front center console, you may have a well that should nicely fit a small sharps container -- so you don't have dead strips (lancets, etc.) floating loose around the cabin.
Hopefully these photos will give you some ideas for making pre-drive and rest-stop testing more convenient, and speeding access to quick treatment for sudden lows.