<p>Based on the discussion in comments above, my current suggestions are as follows:</p>

<ol>
<li><p><a href="https://stats.stackexchange.com/questions/tagged/meta-regression" class="post-tag" title="show questions tagged &#39;meta-regression&#39;" rel="tag">meta-regression</a> stays as a distinct tag. Currently <em>all</em> questions with [meta-regression] are also tagged with <a href="https://stats.stackexchange.com/questions/tagged/meta-analysis" class="post-tag" title="show questions tagged &#39;meta-analysis&#39;" rel="tag">meta-analysis</a>, but it's still a useful subset tag to have.</p></li>
<li><p>We remove all instances of <a href="https://stats.stackexchange.com/questions/tagged/fixed-effects-model" class="post-tag" title="show questions tagged &#39;fixed-effects-model&#39;" rel="tag">fixed-effects-model</a> and <a href="https://stats.stackexchange.com/questions/tagged/random-effects-model" class="post-tag" title="show questions tagged &#39;random-effects-model&#39;" rel="tag">random-effects-model</a> from [meta-analysis] threads. We also remove most instances of <a href="https://stats.stackexchange.com/questions/tagged/mixed-model" class="post-tag" title="show questions tagged &#39;mixed-model&#39;" rel="tag">mixed-model</a>, leaving only the ones that are really about "standard" mixed models <em>and</em> meta-analysis.</p></li>
<li><p>We  create the following three tag synonyms:</p>

<ul>
<li><code>[meta-analysis-fixed-effects]</code> $\to$ <a href="https://stats.stackexchange.com/questions/tagged/meta-analysis" class="post-tag" title="show questions tagged &#39;meta-analysis&#39;" rel="tag">meta-analysis</a></li>
<li><code>[meta-analysis-random-effects]</code> $\to$ <a href="https://stats.stackexchange.com/questions/tagged/meta-analysis" class="post-tag" title="show questions tagged &#39;meta-analysis&#39;" rel="tag">meta-analysis</a></li>
<li><code>[meta-analysis-mixed-effects]</code> $\to$ <a href="https://stats.stackexchange.com/questions/tagged/meta-analysis" class="post-tag" title="show questions tagged &#39;meta-analysis&#39;" rel="tag">meta-analysis</a></li>
</ul></li>
</ol>

<p><strong>Update: (2) done by @mdewey, (3) done by @gung.</strong></p>
