Hey Julian,
Are you planning to keep using the battery in the caliper? Wouldn't it be possible to hook up power from Arduino to supply the caliper with power, getting rid of the battery?
A fresh 3 V (nominal) button cell (e.g. CR2032) may easily measure at up to 3.5 V (no-load) when you first unpack it. I'm reasonably sure a caliper would work fine on a 3.3 V power supply.
I don't know if these links will be of any use to you, but here they are:
Caliper2PC is an interface box for connecting various kinds of linear encoders. I guess it first started off in a similar way as what you're doing now, but by now it supports all kinds of encoders: TTL/quadrature signal glass scales, magnetic scales, rotary encoders, iGaging scales, various kinds of calipers, Mitutoyo Digimatic calipers and indicators, even analog sensors. The author is pretty responsive and helpful, perhaps you might want to discuss with him what you're doing, maybe he could give some helpful tips. I personally have two of these Caliper2PC boxes, one for the lathe and for the mill. I'm using a couple of second-hand Thinkpad X230t 12.5" convertible laptops/tablets as displays.
Keep us posted on your experiments.
Best regards,
Gene
