It would be worth having an extra chore if you think it's worth having cleaner eggs and not having to clean poop out of boxes.
The hens are sleeping and pooping in/on the boxes and that's why there's poop there. It's a bad habit and one you
should try to discourage. Whether it's risen to the level of importance
enough for you to do something about is your decision. It's definitely a contributing factor to the fly problem.
With the warmer weather, flies are everywhere and their life cycle runs fast! Depending on the type of fly you have, a life cycle usually measured in days, allowing the chickens to scratch around and eat the larvae before they start causing problems, is now measured in hours (or is much, much faster). There are more flies being drawn to your birds than before, and they are reproducing at a faster level than before.
I make sure I have "mucking about" clothes that I use for poultry and
gardening, wear gloves, and do very lackadaisical care of my birds. I do a twice a year cleaning of the main congregation areas, do "spot cleaning" as and where needed, but my flock has a very large space for ranging and I tend to lose more birds than people with confined runs. It's a trade-off. We all make the decisions that suit us and our circumstances.
Flies are a problem. Black flies can kill chickens if there are enough of them.
If you were able to stand the smell of it, I would suggest putting a baited fly trap at a different spot in your yard, to draw the flies away from your chickens. I know of people who have good results with fly paper in really bad areas, but you have to deal with fly covered fly paper as clean-up for that. It might be a bit much.
Cedar is bad because it can damage lung tissue in confined spaces. Yes, it's good as a deterrent for a lot of insects, because of the polyphenols which is what makes it so good at it's job.
Whether or not you use cedar shavings is a personal decision based on what you perceive as a benefit to your birds and the price you are willing to pay for what you get. I put that in the same category as feeding a "layer bird" bagged feed to cockerels and roosters. They can eat it and be fine, until the calcium solidifies their kidneys and they die. Some people make the decision to feed a layer feed anyway, with the knowledge that a rooster will not likely live past 5 years. Again, it's a personal decision.
If you have a routine that works and that you use year-round, I wouldn't change it. It works for you. Your birds are used to that level of care and attention. The only reason it stopped working is because your routine was out of whack and you now have to catch-up to what it was. There's going to be some yucky times while you bring everything back into balance, but the summer will end, thankfully.
Once you get the cleaning routine back, it should be fine. There will be a slight delay as you get the current fly population under control, but it will happen.
Old fashioned and less invasive ways to control insects - whitewashing your coop, roosts, nest boxes and all twice a year; doing a deep cleaning twice a year and scrubbing everything (prior to the white wash and then letting things dry in the sun); keeping the ground around your coop and run as dry as possible to prevent stagnant
water areas; keeping the poop buildup down through a regular level of cleaning maintainence.
Any or all of that could help.
At least fly season will pass. It'll be colder and frosty before we're ready for it!