Out the position you named the only one they may look at is a cheap vet QB between the 3-7 million a year and a guard. Maybe a splash at DT, but the rest will mostly come via the draft I think. So that’s enough money the way the Saints do the first year of contracts.
If you rely on the draft for all that you put yourself in a bad position. If you predetermine what you must draft you reach. Drafting well is the most paramount thing we can do right now.
To reduce the first year you need to sign long-term contracts. So 1-year deals aren't much of an option. Void years help but go against the whole premise of this. Even then you are looking at 3-5 mil per contract in the first year for any modest contract that has any guarantees.
Why do this to yourself? Just restructure Carr and give yourself breathing room. You're still set to rebuild in 2026 either way.