I think that any card beyond open water certified (in recreational diving) is superfluous. Any experienced dive master or instructor should be able to see if you are skilled enough to dive by yourself.
Something like a Solo Cert is just a way for the operators to say NO first without being jerks. They can (at their discretion) allow you to dive however you want, once you've demonstrated the skills required, with or without the card that says so. If you say you have 1,000 dives, and can't maintain buoyancy, then I'd have to guess you were lying, and they would probably NOT let you solo dive. If they see you are competent (on the first day of a 5 day trip) then I'd have to guess they'd let you solo dive - with or without a card.
I have to disagree with you, my friend (missed you in Long Beach).
I think THE most important thing to know about a diver (or a diver about themselves) before allowing them to dive solo is how they respond to emergency situations. If they quickly panic, I would not want them diving solo off my boat (nor would I want them as a dive buddy). If they respond in a level-headed, rational way and move towards correcting the situation, then I'd think they were far better candidates for solo diving.
This is something many divers don't (yet) know about themselves. After 50 years on SCUBA, I've learned that I almost always respond to emergencies with a clear head (state of denial?) and instinctively initiate actions to resolve the problem. The one time I truly panicked was at the surface in a 3-4 knot current when my pony reg got caught on the current line and I kept getting pulled under without sufficient air in my main tank to breathe from and no way to open the pony valve while hanging onto the current line with one hand and holding my housing with the other.