What you want is about synthesizer features, not soundfont.
For example, only one sound can be played when the synthesizer is set to MONO.
If note Priority can be adjusted in MONO mode, there may also be settings such as Last-pressed, First-pressed, Lower-Key, Higher-Key.
maybe something similar to what you said can be done if right hand is set to POLY and left hand is MONO in split mode.
There is also a Sostenuto pedal. It used to be used for a situation similar to what you want. Unlike the sustain pedal, the sostenuto-pedal keeps the notes of the keys already pressed at the time it is pressed, and does not have an effect on the next ones. On older pianos this pedal would only work for the left side of the Keyboard, but on MIDI it would work anywhere. For example, you played a bass note in the left hand and pressed the sostenuto pedal just before releasing the note, this note is held as if the sustain pedal was pressed specifically for that note. This feature is especially convenient for the pianist in Stride-style playing (or in works where the left hand uses jump areas for bass and chords, such as Chopin's works).
What I have said here may not be of use to you. But it might give you an idea of the options available for a synthesizer (software or hardware that interprets the soundfont). NOTE: Not all synthesizers may include Split and Mono features. Even if it does, not all priority options may exist.