You indeed cannot use Letters feature for what you are trying to achieve, since you will indeed influence all assignments.
You have to be very creative here and create bunch of Scales with different % breakdown. This will be very hard and may be not even possible if you need to figure out a lot of those and if you later need to aggregate such items.
Here is an example:
Create Scale 1 that will be later used for Assignment 1
F, D, C, B, A.
Create Scale 2 that will be later used for Assignment 2
F, (do not use), D, C, (do not use), B, A
You can see that I have inserted some extra items inside, so it would change my % breakdown.
I have attached a screenshot of what you can get at the end (assuming that scales are included in aggregation, and if aggregation is set to SWM).
Even from this screenshot you can tell that calculations can be confusing.
I would probably go easier route (to me) - second part of the screenshot.
Grade your assignments the regular way with real numbers and display only them and may be Percentages in the gradebook. Use Feedback area to type corresponding Letters manually for each assignment (you can do this either via Assignment tool or Gradebook)