I would apply for the BCE and wait for the CSP, maybe go for the Freedom first to build that relationship.
I tried several times after getting my Zync to get the BCE, but kept getting denied. All the times my account was less than 6 months...then I went on a hiatus from credit, reapplied with my Zync being over a year old and was approved.
I would wait a good 6 months before applying for either the BCE or CSP.
I'm not certain that the hard limit Zync is a no fly zone for other applications anymore. There were a few folks I believe who reported that was no longer the case after the card was discontinued. It's worth taking a look at Amex posts from November or thereabouts.
As for length of history with Amex, we've had two recent people approved for BCP's with ~4 months history on Zyncs. It's absolutely a YMMV thing, but I don't think there's a hard and fast rule when it comes ot Amex underwriting and their internal score calculations.
Like others have said, if you get denied, 99.87% of the time it's just a SP anyway, and the other fraction of a percent is if you're a marginal application; however, after today I'm really going to have to rethink what's marginal when it comes to Amex and my own BCP laughable approval.
Laughable ??? How so ???
650ish FICO approval, or at least similar since that's both my EQ and TU roughly and my EX report is nearly identical.