No system can be perfect. As long as we have electricity near water there will be an electrocution risk.
The OP has a system to be repaired and a customer willing to invest the money to repair it.
What is the best practice to practically minimize the risk presented by the customers pump?
Installing wire with intact insulation and an EGC is code required and IMHO a great first step. Is that sufficient? Simply doing regular maintenance on systems is the most important safety measure.
Does wire type make a safety difference? I'd imagine (but have no real data) that something like SE cable, where the concentric neutral is used as EGC would be desirable.
Protecting that cable in conduit may not be required, but is probably a very good practice since the added costs get balanced by reduced maintenance costs. A conduit may even be cheaper for the customer long term.
Adding a GFCI might actually reduce safety, if nuisance tripping means the protection gets bypassed. Would it be better to install GFPE? What about placing the GFCI near the end of the run? Would fault monitoring (some sort of leakage current meter) make more sense than a leakage interrupter?
What about bonding? Code would require the EGC for this circuit to be bonded to the supply system ground and thereby to the mains neutral. We know that mains elevated neutral potential can cause shock hazard. Would breaking this normally required bond improve safety? How would you do this yet be code compliant?
Jon