Please indulge me be allowing me to start off with some definitions.
Sprints are generally 1-3 weeks long, happen at a regular cadence and don't have anything to do with ongoing projects/releases other than the fact that Stories related to a project are added to a Sprint.
Projects have phases and milestones, can span multiple sprints and can be Gantt charted easily within Aha.
The problem is, Aha treats Sprints and Projects as the same thing. They are not and when I add Releases for project planning purposes, those releases get confused with my Sprint releases making a mess of my Board.
Thank you for the idea and taking the time to explain it well!
Because Aha! is so flexible, there are a number of ways to represent sprints in Aha!, as separate from releases. This article goes into detail on the option of using a custom field and syncing that with Jira.
I encourage you to reach out to our customer success team at firstname.lastname@example.org and they will get back to you quickly to work through some options that might work well for you.