I currently use Thunderbird to organize my tasks. I have them pinned to a calendar by their due-date and in a side panel too. However, a major limitation of Thunderbird as a whole is the fact that I cannot attach a start date to a task without it appearing several times on my calendar for each day that it can be worked on. This is pretty annoying and I only want it to appear on the calendar for the date it’s due. I also want my task pane to sort of show the number of days it’s due, whether it can be started yet, and if not, how many days until it can be.
Afaik not many task organizers can do something this complex. I’ve used KOrganizer and its forks in the past but there was too much friction in using it that I switched to Thunderbird.
At one point while looking for a calendar app I needed one that could import events from a text file (not ics) and khal was recommended. I was able to import 250 events in one command. I didn’t want a cli calendar, but I ended up just keeping that one installed along with todoman for task lists. It isn’t ideal, but I haven’t noticed the problem you have said about due dates and start dates.