A bit more progress... 

It appears the payment settings for the memberships has to go through the site administrators account settings, and is unrelated to the Stripe Connect module. I have searched these forums and GitHub pretty thoroughly and do not believe I have seen that stated... maybe I missed it.

I started a Chargebee account, connected it to the same Stripe account, entered that test info into the profile payment settings, and it appears to have worked fine on the first try.

(Btw, for others that see this troubleshooting, the 'site name' that is requested in the profile payment settings for Chargebee, is only the subdomain of the chargebee account. IE;  subdomain.chargebee.com)