You can make it without any additional final changes, but in reality what you can do is make two changes in the 5 minute grace period. This is a workaround and a somewhat taxing one at that, but it's functional and I do it all the time.
First, edit your question with some very small edit. It doesn't matter what it is. You should elect to add your new edit summary at this point - thanks to this new featurethanks to this new feature, it will stick around. It'll also make the job easier since you can just edit it in place rather than re-type the whole thing.
After submitting that edit, start editing again and simply remove the change you made in the previous edit. The end point will be all the content of your previous edit, but you'll have the revised summary you wanted. If you didn't elect to add the summary in the previous step, by the way, you'll obviously need to add it in this revision. Otherwise it'll be all for naught!