Variance in Pressure Switch Deadband

My client has 27 small reactors. The gas blanket pressure in the reactor is controlled by a pressure switch that drives a solenoid valve. It turns out, after some significant data collection and analysis that the gas blanket pressure needs to be kept in a fairly tight band, otherwise the process reaction does not progress properly if and when the pressure falls outside a pressure band.

The issue is the variance of pressure switch deadbands from switch to switch, for the same model pressure switch. The pressure switch cut sheet lists a deadband range for any switch. Apparently, what appear to be identical switches can fall anywhere within the deadband range.

4 vessels (2 well performing, 2 badly performing) were outfitted with pressure transmitters to monitor the pressure. The well performing reactors stayed within a given pressure band, the poorly performing reactors were outside a given pressure band.

In the poorly performing reactors the band was too large allowing the pressure to drop, resulting in a wider pressure band with less frequent cycling, but poor performance.

Yes, we know about pressure transmitters, electronic PID or on/off controllers and respective valve actuation, but given the size of these reactors and the respective gas useage, that the process doesn't need constant pressure, it just needs pressure maintained within a consistent band, classic on/off control.

Electronic control seems to be an expensive upgrade compared to getting consistent switch deadbands.

Anyone aware of pressure switches with consistent, repeatable deadband?