There are quite a few 2.0 DIN head units to choose from with the features you are looking for. Crutchfield is always helpful and they usually carry the better brands, but there are alternatives too. The "static" you are hearing is probably from the head unit volume control, but without connecting another head unit to the system, you cannot tell.
This is one of those circumstances (especially if you cannot do any of the work yourself) where yanking out the whole system is cheaper than troubleshooting the issue to find out exactly what is not working properly. The Bose amps are equalized for each model vehicle, taking out the Bose amps and speakers will allow you to put in aftermarket speakers with a more "normal" impedance, but you will loose the equalization. Most Bose speakers are 1-Ohm, instead of 4-Ohm.
Putting in an aftermarket head unit and new speakers will address the factory equipment and no more headaches, but you'll loose a lot of equalization that simple Bass and Treble controls will have a hard time restoring. Now of course this is all subjective and certainly depends on each individual listener.
In my '92, which came with a Bose CD / Tape deck, I removed this unit and installed a 2.0 Din navigation unit. I wanted to keep the Bose amps and speakers so I made an adapter for the head unit RCA line outputs that would allow me to drive the Bose amps. The rear speakers are only 6.5" speakers in ported enclosures. These speakers provide rear-fill and get cut-off somewhere in the upper midrange region.
The front speakers are also in tuned enclosures and do not sound too bad, but the tweeter placement is terrible from the factory. when your leg is fully extended, it conveniently blocks the tweeter, thus eliminating any high frequency response. I addressed this issue by disconnecting the OE tweeter in the front enclosure and placed small 19mm dome tweeters in the driver and passenger A/C vents.
The Bose system actually sounds fairly good (for what it is), but again, sound is a very subjective matter. This was actually an experiment to see how good the Bose system could sound and I also did not want to "gut" the OE audio system. Most people who hear it think I took all the OE equipment out.
Sure, the Bose amps are problematic (if they are older), but mine were all replaced prior to me buying the car, so they should last awhile and not have any of the "common" problems. The speakers usually last longer unless they get wet or are abused (easily done).
Bose systems for the C4 varied by year so your system may not yield the same results as mine, but if you like to tinker and are handy, the Bose system (speakers and amps) might give you the sound you are looking for.
CG