Documentation for multilevel CFA/EFA

There is a long long history of spacing longitudinal data in wide format to make rows independently and identically distributed (iid) for the purposes of confirmatory model estimation. To run in OpenMx, set up your data so that it is 48-54 variables wide, with the first 16-18 being the time 1 variables, the next 16-18 as time 2 and the last 16-18 as time 3. Make equality constraints such that whatever structure you apply to the time 1 variables you also apply to the time 2 and time 3 variables. Congrats! You've solved your clustering issue. Let whatever latent variables you have at each time point vary freely with latent variables at all others (you'll typically not allow residual covariances, but constraint residual variances to equality over time).

EFA is a little different issue. Wide format data won't work, as you can't make the required equality constraints. You're correct in your assessment of the impact of clustering on standard errors; if you have complete data (with exactly 3 observations per person), that might be your only problem. If you have any missing data, you're also likely to get some additional bias in parameter values. I hereby refuse to confirm your EFA suspicion, though I'll do some reading on clustered EFA if I have time. Feel free to share any articles you find on the subject.