As noted in this duplicate question, it's possible to edit the edit summary during the grace period if you make at least one other post at the same time. However, if the edit is all correct apart from the summary, it's strange to force a pointless edit just to be able to change the summary, and worth making the change to the edit summary itself work directly.
This feature request requested combining the edit summaries of the two edits, but was declined due to misunderstanding how a grace period edit works. The sentiment is still correct, though; what should happen is that a change to the edit summary during the grace period should be considered as an edit to the post, even if the post itself doesn't change.