I have to agree with everyone else about the compressed hours. It can work well, but usually when most people do actually work their contracted hours. If contracted hours are 9-5, 5 days a week with an unpaid hour for lunch everyday, ie 35 hours, compressing that into 4 days by starting a bit earlier, working a bit later and working through most of lunch is pretty easy to structure and be visible as well.
But if contracted hours are a notional thing on a bit of paper and in reality most people work more like 45 hours, compressing that isn't usually that realistic anyway and the perception from other employees will be that 'everyone works late and gets paid the same, but Cokie gets an extra day off every week.'
I've turned down several compressed hours requests before. People would approach the employer saying for example that they will work through their lunch so they can leave at 4 rather than 5, as that will add up to the right number of hours, neglecting to remember that to do their full time job before maternity leave they were working through lunch already and leaving at 6, and that's what their colleagues are still doing.
Whether a long hours culture is a good thing is a different matter of course, and whether people's workload is too heavy as well. But that is the reality you are working with in your job at the moment.
In terms of what you can do, well take the initiative. Instead of asking your boss how he is going to reduce your workload by 20%, you put forward a proposal as to how it will work. Unless there is a job share situation, reducing workload just like that isn't often an option anyway. If there is a full time workload there, where will the rest of it go?
Instead, for part time flexible working requests, usually the best way to get them approved is to demonstrate how you can do the job in less hours. This would often be by identifying tasks that are unnecessary, or can be done more efficiently, for example.