Hi @JaspalX, I am always happy to see people working on underwater caves as I had spend a fear amount of time doing so.
It is not an easy problem but I think that you are on the right track for your task. Range measurements form the Ping shouldn’t be a problem and your accuracy will depend from the distance from the walls and the beam footprint at that point. I will agree with @EliotBR to have a second look at the Ping360 as it may give you more information and will remove the need to synchronize 4 sonars.
Normally in caves the major issue is the horizontal localization and 3D orientation of your system because you want to know how to position your measurement to your map.
The orientation can be solved with a MEMS roll/pitch/heading sensor and a pressure sensor. Just take care with the heading because as @EliotBR mentioned, you can get errors from metallic structures (pipes, supports, cement, etc.) or natural iron in the walls.
For the horizontal positioning; In case you have fixed reference points or you know the distances from where you taking the measurements, you are all set! If not, then becomes a much more complicated and expensive task. Maybe this thread gives you some more helpful info.