Here's an extract from the TSR3 of the old 2016 franchise which promised services to Colchester Town on Sundays.
This also promised direct to London 3tph to Southend, 1tph to Braintree and 2tph to Norwich (3tph to Ipswich).
If the stops between the Ipswich stopper and Clacton stopper were balanced - perhaps the opening of Beaulieu Park would do this - it is possible to have 2tph to Colchester Town connecting to both London services.
You make the Clactons leave later to meet their geml paths and you then have the Waltons to Colchester, calling at Colchester town. And then have no Colchester to Colchester town shuttle. This would require 2 units, one more than currently
Marks Tey would then get a 15/45 separation between services. Chelmsford would then get 20/40, as on Sundays it only receives 2tph. This also requires 3 units, but they could be used to provide a second train per hour to Colchester Town during the long turnaround time to combat this.
Exchanging Hythe, Alresford and Great Bentley stops for Ingatestone, Hatfield Peverel and Kelvedon stops for the Clacton services would cause the 30 minute gap between Up/Dn services at Colchester to become the required 15 minutes separation between Up/Dn as on the weekdays. Extending the Walton stopper would then give intermediate stations between Clacton and Colchester a 2 unit service at exactly 30 minutes opposite to weekdays.
This would also stop the Norwich service catching up the Ipswich stopper so a 2tph service London-Ipswich runs 5 minutes apart.
Anglia really has a poor Sunday timetable, which is absolutely not limited by engineering work but by questionable timetabling to which I cannot see why certain decisions have been made.
Realistically, none of the simple ideas above will ever happen and even a barebones 4tph total service to London will continue to find itself running at minimum headway, 3 minutes apart for years to come.