Hi Jodi,
We just submitted a manuscript that mentioned the issue of direct t-tests versus omnibus F-test guided method, so we may receive a similar repercussion to what you just did. :)
To pacify the reviewers, you may consider running ANOVA. If no inconsistency occurs, all is good. There are two possibilities that may show up: 1) F-test is significant, but none of the individual t-tests; 2) F-test is not significant, but at least one t-test is. These two cases are not expected to occur often, but if they do, it may indicate something worth further investigation, such as violation of the assumptions in ANOVA.
Hope this helps,
Gang