Lets imagine you check your email 4 times a day instead. In an 8 hour workday, you would check it around once every 2 hours. So the absolute maximum time your client would wait for a reply would be 2 hours during working hours. Would your current clients find this unreasonable?

There are not many issues that justify a "NEED A REPLY THIS VERY SECOND" response. You should find that most of your clients aren't sitting at their inbox awaiting your reply, but also get on with their other work. For emergency situations, an emergency number to call if they need a response might be the answer, but stress it's use only for dire emergencies that are costing them real money if not fixed immediately.

This means you can have dedicated time focused on emails, allowing you to form better replies. Cutting back to 3 times a day would be even better. One when you start, once at your lunch break, then once at the end of the day. With an 8 hour work day, 3 times a day is still only a 2 and a half hour maximum wait time.