Negotiate a financial aid package based on…what? If the issue is your kid gets accepted ED, but can’t afford to attend, the college will allow you to withdraw from the ED acceptance.
If you want the school to RECONSIDER (note…not negotiate…this isn’t a used car sales), you would have to have a reason for asking them to do so…loss of a job, some medical issue that is costing you money that isn’t reflected on your financial aid application forms…or some other substantive change in your finances since your Profile and FAFSA were submitted.
Some of these generous schools WILL reconsider a financial aid offer if you have a better one from a peer school…but when you apply ED, you only can apply to one school…so you won’t have anything for the college to look at and compare.
And here is the real rub for you…the ED net cost could be the very best one your kid will see…and if you decline it…you can’t get it back. OR it might be the worst one. You will never know if you accept the offer…because you will be required to withdraw all other applications and acceptances.
I will stick with my first answer. It sounds like finances are a significant consideration for your family. This NPC is giving you a range of results. For all practical purposes, assume the worst.
Apply RD. My opinion.