4khz? Perhaps you mean industrial servos?
Normal R/C servo updates are every 20msec, so only 50hz.
Digital servos can operate at a max of about 300hz.
This might seem too slow, but is in line with how fast you can move your hand and the servos speed. With a fast servo the elevator keeps right up with control inputs.
This was certainly the case with the indoor model, to me it responded just like the regular control version.
In this system the update rate is about 160hz, based on having enough time to output the three 1-2msec servo position information.
Ultimately the goal would be to go to 250hz, but that would require a more complex interrupt handler to be able to output all the servo signals overlapping each other.
Either that or use a micro with multiple hardware PWM outputs.
The bellcrank position is sensed and all the calculations done as part of the main program loop. This takes ~1.5 msec, faster than the servo positions can be updated.
The sensor used is not a rotary one per-Se. It only becomes one when installed between the magnetic field that rotates with the bell crank.
Might be why you had trouble finding one in your search

Part number is SS494B, chosen for its high sensitivity and ratiometric output.
High sensitivity translates to good voltage swing and the ratiometric output means it behaves in circuit just like a pot would.
This, combined with using supply voltage as the A/D reference, gives supply noise/variation rejection to the crank position.
Spec sheet is here:
http://sccatalog.honeywell.com/imc/printfriendly.asp?FAM=solidstate&PN=SS494BIt measures flux density through the face of the part. At zero flux the output is Vcc/2.
It and the magnets are set up so neutral bellcrank has it at right angles to the flux lines, so no flux through the face.
Rotating the crank puts the flux lines at an angle to the face, so flux density is proportional to the bellcrank deflection.
By the highly scientific method of trying the magnets we had on hand and the spacing between them
we settled on ones that gave full sensor output at the crank deflection we wanted to have.
Pat MacKenzie