I agree with most of your post except means testing.
Means testing would penalize those who were/are prudent and saved for retirement and reward those who were/are careless and did not save for retirement. IMO if you have means testing, it would simply further discourage responsible behavior - one might as well spend and enjoy during their working years and SS will bail them out in retirement. Is that what we really want?
I think there should be means testing AFTER the SS recipient has been paid back his contribution + employers contribution + a reasonable investment return say about ~ 7% - the long time equities return. At that point, the recipient has been effectively paid back and monies received after are in fact redistributing income from others and he/she should not be eligible if of sufficient means.