You can try the Vibrato algorithm and see if you like how that sounds. The default preset “Swamp Moon” has the expression pedal mapped to the intensity, so at the heel position there will be no effect, and you will hear more of the the effect as you adjust the pedal towards the toe.
Quick question: How gentle of a pitch bend do you have in mind?
The Vibrato algorithm (Manual assigned to an expression pedal) just might do it for fractional-semitone bends. The H910 / H949 [Modern – Splice; Pitch Control – Smooth] can be used for much larger bends, but it’ll also go ‘gentle’. Keep in mind (with the latter) the MIX will have to be 100, and your tone will change.
As for the pedal steel comment, it reminded me of these presets. One uses PitchFlex; the other two HarModulator.