meta-analysis vs. random effect combined analysis

I have data from 200 similar studies, all measuring the same effect of a continuous independent variable on the same continuous response. I say similar because the designs are different (split plot vs. rcbd) and the levels of the independent variable is not the same across all studies.

I have been reading about meta-analysis (use of effect size as response variable) and the use of mixed models.

I have been thinking to use a mixed model (there is hierarchy in my data - year, study within year, replication within study within year) because I find it difficult to report and interpret the results in terms of effect sizes.

One issue, from what I read, is that sample sizes among studies differ (n=6-192).

I read that specifying the correct random effects that take into account the between studies heterogeneity, along with Satterthwaite or Kenward Rodger degrees of freedom, "correct" possible issues from the sample size differences.

Is that true?

Any help is much appreciated.