What additional electronics are required for construction and use of a 240-cell Ni-MH battery pack?
I doubt you need to do any balancing. NiMH are somewhat tolerant of over-charge, so they will tend to self-balance during the normal charge process.

It would be a good idea to monitor temperature so you can shut down charging and discharging if any of the cell gets too hot. If there is one bad cell anywhere in the pack as it ages, that cell could get very hot during charging. The charger should definitely be designed to detect fault conditions such as failure to charge, failure to terminate charge in a reasonable time period, etc.

If you want to avoid the complexity of monitoring temperature for 240 cells, a carefully chosen PTC on each cell might be a simple solution to the over-temp problem. PTC's respond to both heat and current flow. As they get hotter, their ability to pass current without tripping gets less and less. So if a cell over-heats during charging, the PTC may very well trip before there is danger of fire. You will have to deliberately overcharge a pack to test this and make sure it is safe. Some PTC's are available to act as straps that you weld to the battery in place of a solid metal tab. This puts them in excellent thermal contact with the cell, and is probably the best way to do this.

There are also very small thermal switches which can be bonded to each cell, similar to PTC's but they don't have any over-current protection function. Just mentioning that in case you are interested.

At the pack level, you need a robust fuse. This could possibly be external to the pack. But it should be placed so that a short circuit which bypasses the fuse is very unlikely. You DO NOT want to be nearby if this pack is shorted out.

The maximum interrupt current of the fuse should be very high, because the short-circuit current of a 24P NiMH pack will be very high (maybe 500 or even 1000 Amps). You should be looking at large marine fuses. Note that the interrupt rating specifies the largest fault current that the fuse can safely interrupt when it blows. If you run more current through it, it may basically explode when it blows, throwing hot shards in all directions. This is why you need a large, robust fuse.

I do not believe unusually precise matching is required for paralleling cells, but some form of over-current protection MUST be supplied for each parallel cell. If you use a PTC, as mentioned above, this can provide the over-current protection.

There are a lot of things that can go wrong with any stored energy system, and large battery packs are no exception. They can cause a lot of damage. Mainly through fires. I have tried to share my thoughts on your question, but all responsibility for making sure it is safe is on you, not me. I definitely believe NiMH is easier to make safe than LiIon, but there are a lot more parts available for LiIon. So if you cannot succeed with a simple NiMH, consider a LiIon solution instead.

Note that you are probably going to need a custom charger for NiMH, because the charge termination method is different than other chemistries.