There is no separate setting to control intervals for when push is enabled/disabled.
But the night mode is a reasonable mechanism for that. I don't understand why you dismissed that right away. It has a separate setting for disabling Push (have you looked?). If you keep everything else enabled, and only Push disabled during the "night" time, you'll get the effect you want. And set the night to start at 8 and and at 16.
There is, however, a caveat that I'd test if I were you (I remember some discussion about this in this forum but I don't remember details). The night mode was originally designed to roll over the midnight (i.e. it starts one day and ends the following). I would check if this works correctly when the beginning and the end are on the same day. I'd expect it should, but just in case.
One more thing: IIRC, the app-wide "night mode", if enabled, disables sound notifications. If you long-press on the specific account and choose "Special Settings" -> Night and Weekend mode, - then you have a separate option to enable or disable sound and vibrations during the "night" mode. So, if you still need notifications during this period of time (e.g. if you have a scheduled sync on your phone and you still want to get notifications on your phone, just not Push), you can use this way to set the night mode.
Alternatively (if there are bsome other constraints that you haven't mentioned), you might look into using Tasker app - it probably has the functionality to change Aquamail's configuration based on the time.
