Can hall effect sensor replace 50K linear potentiometer?

[FuZZ1L0G1C]

Preferably need non-mechanical sensing.
Hi, I'm trying to design an electronic treadle-pot that can vary a resistance from 0 ohms to 50K (linear taper?).
Input is 5V DC, output varies according to variable resistance.
1K series resistor appears to be a current-limiter (R=min 1K).
Although web-search showed only a 10K pot (retail pedal), Roland EP7ii-e specs show 50K.
To avoid difficult-to-make gears and mechanics my idea is to use Hall-Effect or similar to sense distance.
Guessing about 10mm-40mm.
As seen in artwork, mechanical rubber idea slipped up (pun intended).
Various others also shown as (theoretical) ideas.
Never used hall effect devices so no idea if it varies or just switches.
Electric piano is Roland EP7ii-e.
If successful, plan further foot-controller project for 12VDC 3A (max) mini-drill.
Apology: As graphics varied from mini to huge, I had to resize PNG's to join into one.
Then to reduce byte-size converted to 8-bit greyscale JPEG.
As a result, bottom JPG's came out blurred but still readable.
Any suggestions welcome.
EDIT (added later):
I did more research on hall-effect sensors so a bit clearer now what it does.
Wiki gives technical description while https:\motor...? describes practical applications and simplifies function.

 

[Bluejets]

There are analog type hall effect sensors but I think you may be trading one form of operation ( mechanical-simple) for the other (hall effect sensor- complex) when it comes to matching the latter with an already developed product.
I suspect you will still need a certain amount of the former in the design anyhow.

 

[Alec_t]

I think you've got your Wiper and Dn connections transposed in the first schematic.