Diy slider potentiometer?
Since it's for a musical MIDI application a smooth response may help you justify an analogue potentiometer. The simplest, which you have already considered, is a 10k rotary pot with belt drive.

Typical 1-turn pot track swept angle is 330°.
You're looking for 25 cm slide.
From \$ s = \pi d \frac {330}{360} \$ we can calculate the required belt pulley diameter, $$ d = \frac s {\pi{\frac {330}{360}}} = \frac {250} {\pi{\frac {330}{360}}} = 86.8 \ \text {mm}$$

The advantage is that all your quality and wear issues should be sorted by the manufacturer and would be easily replaced if it broke. You could make this with a string rather than a belt as used in old fashioned variable capacitor radio tuners.

Figure 1. Image source: EDN.
You might be able to simplify further by using a multi-turn pot - a 10-turn, for example. A direct winding on a 6 mm shaft will require 18.8 mm per turn so ten turns would give you a 180 mm slide which might be good enough.