Could it be that the "broken" genes serve legitimate purposes that are simply unknown at this time?
Yes that is possible. However, there isn't any hint of it yet.
There was (referenced elsewhere I don't have it) a study where large segements of mouse "junk" was stripped out. IIRC, the result was -- no change. The animals seemed perfectly normal.
This is the type of experiment that will have to be done over generations to be sure there is no effect but it is indicative.
As I noted, if there is no significant cost to carry extra DNA then there is nothing to remove it. With that the case we can expect DNA to pile up that would be really non functional.
This would supply a source for new funtions with further mutations of course. It may be that this is a long term advantage that actually selects for having "junk" DNA but I'm n ot sure that can be the case.
I expect the regulating parts of non coding DNA will be shown to have certain properties. I will be very surprised if those include looking just like a working gene that has had a hit by a mutation.
You may continue to hope for some new discoveries in this area but I don't see it likely that it will help you. These same discoveries are very likely to further strengthen our understanding of how we and chimps evolved from a common source. You should not pin your faith on what will be found out in genetics.