Prior to the current side-scan sonar search using the Bluefin-21 getting underway, the Ocean Shield spent some days towing the TPL equipment. While this was happening, HMS Echo moved into the same area when appropriate to undertake a comprehensive analysis of the water conductivity, temperature and depth using a CTD probe to measure those variables and determine the affects that would be encountered by the ULB acoustic pings on their travel to the surface.
They also used an Expendable Bathythermograph to further check the accuracy of temperature and depth recordings, while their HiPAP (High Precision Acoustic Positioning) sonar was being used outside its normal operating parameters to listen for the aircraft transponder.
I doubt that chucking another ULB into the water is going to tell them anything of relevance they don't already know. There is adequate evidence also available from the initial recordings of the ULB pings to confirm that their acoustic frequency was decreasing at a rate comparable with that of a similar battery of its age and operating time combined with the local water temperature.
A Dukane spokesperson has previously acknowledged that the 33.331kHz pings were what could be expected. The oscillator is not Xtal controlled, being a resistive/capacitive oscillator with the low Q transducer forming part of the circuit.