The problem is that the CEO has access to MySQL's show processlist; pooled connections show up as idle threads in that and Apparantly That's Bad.

First, regardless of what technical problems you're having the CEO shouldn't be involved at that level. If he is, what is he paying you guys for?

Now, assuming you're dealing with someone who should be looking at the processlist -- and since he's The Boss™, he gets to decide that he is that someone -- it might be appropriate to contrast real production problems that you can demonstrate you are actually having vs. a potential perceived inefficiency.

Is there a slow time or regular maintenance window during which you could try changing the configuration and benchmark it? If so, I'd put together a list of two or three changes you'd like to try -- like bumping up the limits you mentioned above, things you believe won't actually fix it -- and then while you're doing it also try the pooled connections.

And just so I have some frame of reference, what kind of transaction volume (page views) are you doing? I worked on a system with three fairly beefy webservers hitting a MySQL master with five slaves.