Hi Charlie,
As Scott mentioned, there is not really a way to do this in Edit+ at the moment, however it is scheduled to become part of the next release. If you are a Squiz client, you should have access to see it here: https://squizmap.squiz.net/editplus/4108
We're aiming to get this developed for the next big release which will be sometime in March and will be 5.2.0.0.
In the meantime, could you get away with just setting the start time as 00:00 and end time as 23:59? If you are not displaying the time on the front end for these events, that should be ok then. This would make them appear as normal for calendar listings. You could also have a conditional layout to check if the start and end time is that, don't display it on the front end and treat it as an all day event as well. Hopefully that helps in the meantime.
You could potentially also do it with a custom Edit+ plugin, but that would require some extra work and someone experienced with JS and the Edit+ code.