Usually just the tips and not more that 1/3 the length when pushing it from what I've heard. If any are diseased, just keep the healthy parts. As for fitting them through all the holes, l'm not so sure about that. It is better to mostly get the roots to chase the water IMO. Just putting the roots in the net pot with a medium like expanded clay (hydroton) should do much of the trick since it wets by itself wicking solution up when barely sitting in the top of the water level. You don't want to drown roots, especially those injured from cutting and having a lot in the more oxygenated medium is better than under water - by far.

Others may have better experience with what to do with the roots for a big plant, but I would prefer to cut out part of the bottom nd bring a braid of fluffed out root if I had no other choice, and let the plant do the rest. Since you may have a large plant it might be more complicated. Maybe a different medium like a simple perlite bag system, but that's just mulling. My experience was with different plants and although the roots served their purpose initially, my plants eventually developed new white roots and the older ones eventually dissolved away anyway in a great part which as old organic matter provided microbe food, especially those that were under the water level. But I'm just one data point...