HCSR04 ultrasonic sensor as transmitter/receiver only?

I would like to get your opinion on my project and the following approach:
I have an object that is attached to a person's hand. I would like to track this object as the person's hand moves and determine its relative position to three other HCSR04 sensors that will act as receivers. The transmitter is running on Arduino Nano that also has an RF transmitter. It also has a HCSR04 ultrasonic sensor mounted on it that acts as a transmitter. I also have another Nano which is stationary. It has an RF receiver as well as three other HCSR04 sensor that would act as a receiver.

When I want to get the position of the object, the RF transmitter that is mounted onto the moving object I am tracking issues a command. At the same time I would like the HCSR04 to emit a burst. At the same time, the RF receiver on the stationary board would receive this command and the put the other three HCSR04 in listening mode. When each HCSR04 receives this burst, distance would be determined based on when the burst was emitted and received by the different HCSR04s. As for the precision, I basically want to determine the closest sensor to the sound source (eg; the object I am tracking) so I am really just looking for a relative distance to each sensors, I don't need to know the exact distance in mm's.

I know timing is critical but my question is; is there a way to put the respective HCSR04s in receive or transmission mode only? When I am looking at the library it seems simple but I wanted to see if any of you have some experience with this? Does this approach seem feasible to you?

Thanks in advance

You have to "fool" the firmware in the module, AFAIK it's not open source. The only easy way to do it is to trigger all the modules simultaneously, but physically disconnect the transmitter transducer on all except one unit.

To dynamically enable/disable the transducers would be a fairly complex electronics project.

I would like to track this object as the person's hand moves and determine its relative position to three other HCSR04 sensors that will act as receivers.

This has been done many times, and over the years a few commercial implementations have appeared, then disappeared. I recall a pen-sized pointer with a spark gap being used as an impulse source in one of them.

The idea is not difficult to implement, but evidently doesn't work well enough to be practical. Noise from the environment is almost always a serious problem.