I need advice on thermostat probe placement

One of the many reasons you are seeing such variations in that these probes are designed to measure ambient air temperature. This in laymen's terms is the air temp in the tub or temperature created by convection. To measure a "hot spot" which is heat caused by conduction and will be transferred to your snake by conduction, you need a surface measuring instrutment (like a pyrometer). Conduction is the heating of a surface or material by heat exchanged from another surface or material by direct contact.

stable environments can "somewhat" be created in unstable outer environments through the use of multi zone heat. That means you control both the hot and cold ends separately. Even this has its limits.

If you have a tub that needs to be 20 degrees warmer than your outer environment, you can probably pull it off effectively with flex watt. If its more than that, you need to change conditions before thinking about turning up flexwatt to higher temps.