May I suggest keeping an eye on those glue traps as they can accidentally trap beneficial insects that prey upon and eat pests. If there's other bugs like assassin bugs, green lacewings, and lady bugs stuck on the glue traps, and not many cucumber beetles or other bad bugs, they may be doing more harm than good. Here's a neat picture of an assassin bug feasting on a cucumber beetle.
I think there's a couple options to consider for protecting future growth. So the diseased and dead leaves are no longer being a benefit to the plant, harnessing sunlight and making sugars, and are harboring disease spores and possibly other things like cucumber beetle eggs for example. Removing all the sick leaves won't do any more harm than what the diseases and pests have done. Those leaves that are removed really need to be either burned or bagged and taken off site, far away from the garden. You mentioned you have neem oil, and neem can be a great preventative treatment in certain situations, and I think it's worth a try and hope to get good healthy leaves and get some cucumbers to eat.