Automating thermostat min temp and max temp for UI

My zwave climate entities have a min temp and max temp. The lovelace thermostat card reads those values for the slider limits, and I’m trying to limit them to not exceed the opposite system mode.

My train of thought is:
if cooling temp changes, set heating max temp to cooling temp minus two.
if heating temp changes, set cooling min temp to heating temp plus two.

Using the climate set temp value service call does not update the entity, so is there a way to automate that value to the card using card-mod? I’ve been bumbling my way through examples of modding custom cards, but having difficulty finding the right setting to change.