Thing is that shells don't fly 'very fast'... they are nearly universally below 200m/s near their practical ranges for indirect fire ~ only with low angle direct fire over open sites can you expect supersonic flight throughout.

The trajectory is fairly predictable once you have 2-3 points you can rapidly estimate an origination... anything else coming from this region will confirm the exact firing site.

There exist a specialist (but not more complex) series of counter artillery and counter mortar radar that perform this exact function. I think it possible that there is some confusion about exactly what is being discussed, but equally I can see a gun position that was static and a 'nuisance' being pinpointed over a matter of hours or days, even with the 'wrong' equipment...

Flash and sound ranging could give some indication of 'grid square' and then a systematic 'search' with radar of this zone during gun activity should pinpoint the location.

Is it also possible that the Rgt had attached a 'proper' counter artillery radar element, using the ADA net to coordinate with fixed wing strike aircraft?

** And to add to the AD-system as C-Arty Radar... the 'official' Counter artillery radar was a development using elements of the Krug Radar, on an MTLB chassis...