For a 95% CI, how about the straightforward interpretation of a prediction interval:
“There is an 83% chance a replication with the same N will obtain a result within this interval”
To my mind, this is the most useful interpretations. Note the capture rate is not 95% because both estimates are subject to sampling error. I think that means that as the sample-size for the replication grows towards infinity the expected capture rate grows toward the confidence level.
Reference is Cumming & Maillardet, 2006, http://psycnet.apa.org/buy/2006-11159-001.
I’m curious if you object to these or not. I’m also curious if you think the same statements can be made about Bayesian credible intervals. I can’t quite wrap my head around it, but I think Bayesian credible intervals are not prediction intervals,