An ounce of prevention is worth a pound of cure but it is too late for that.....
I bought a moisture trap one time and in it they had a schematic for an air system. The lines were slanted and T'd so that any oil that dropped out of suspension would drain BACK to a low point near the compressor so it could be drained off.
Also, any line "drop" was T'd in out of the TOP of the main line (instead of the bottom) - fluid's don't tend to gravitate UP....
However this usually means you have to redo the whole system - why didn't I find the schematic BEFORE I plumbed it rather than after???.... Typical.
Since replumbing is probably out of the question, you're probably going to have to mount any number of traps in the system.
Better yet, DON'T put the oil into suspension in the first place - perhaps fixing the mofo compressor might be a good place to start....
Tramp oil in the system not only traps itself but it also traps moisture. Moisture and oil plus hot air (compressed air is quite warm) is a PERFECT environment for rust and corrosion and crud to form.
Oil that gets into rubber hose starts a deteriouration process that is not reverseable. It is probably better to toss the hose that to try to 'clean' it... With the cost of hose from Harbor Freight and other distributors anymore, it is a commondity like kleenex to be used and tossed....
If the degreaser idea worked right off, great. But where do you dump the goo that it will dislodge??? Toxic crud blown into the shop is hardly a good place to let it fly. Then, if you merely loosen a remote chunk and DON'T remove it, it will inevitably come loose and create havoc later on.
In a small shop, it might simply be cheaper and easier to replumb. Consider plastic for "hobby" work as it will withstand the burst (under 125 psi working if you buy the right stuff). IT is easy to fab and cheap compared to steel. I"ve had it in my garage for nearly 12 years and asside from the OOPS of overtightening a threaded fitting, it has been trouble free.
But in light of what you've bee through, you learned all of this already,
Regarding the oil separator idea, trap it as soon as possible as opposed to contaminating the system.
You've already outlined the appropriate fixes hence you already know what to do. What more convincing do you need asside from the problems you've already had???
Why should you beat your head against the wall??? Simple. Because it will feel so good when you quit....