The HMv4.0 did not have the (very simple) RC filters on the probes, so the probes were inherently more noisy on those boards than v4.2 and above. Still, the probes should be more stable than you report, particularly ThermoWorks probes.
Since we're talking about an old HM (v4.0?) my first question is, did the unit work properly in the past and this problem crop up later? Or was this HM never working properly?
In general the tips for flaky probe readings are as follows:
Make sure the probe jacks and the few components between the probe jacks and the ATMega are soldered well.
Clean away excess flux on the above components using alcohol (or a flux away product) and a soft brush.
Since this is an older HM perhaps you have corrosion on the contacts of the probe jacks?
Finally, you can add the RC filters to your HM fairly easily which will remove noise from the probes, it's just one resistor and one capacitor per probe. There is info in this thread about doing that to a HMv4.0 and v4.1
https://tvwbb.com/showthread.php?50543-HMv4-0-to-HMv4-1/page3