Is it possible to edit bone positions on the posed (not rest) stance?

Question

EDIT3: Apparently my question is harder to solve than than I expected, so here's my Blend file.

I have a model which is A-posed at rest ("rest", arms closer in angle to the cape bones shown in the final image), and have been using the T-pose ("posed") to modify his mesh. Fixing the mesh makes the arm and finger bones appear relatively incorrectly placed, and I would rather fix them in T-pose to avoid dealing with all the diagonal transforms. In other words, I would like to keep the A-pose as rest and T-pose as posed, but edit the bones from the posed position to have changes appear in the rest position. Redefining the T-pose as rest would require me to redefine the A-pose as rest later. It's possible to edit the mesh in the posed stance by enabling "on cage" (triangle icon in first image) and "edit mode display" (square icon) for each meshes' armature modifier, but is there a similar option for the armature itself?

Armature modifier showing the On Cage and Edit Mode Display options enabled. Normally this modifier only has the Viewport Display and Render options enabled.

This gif shows that the changes I made to the mesh are fairly drastic.

This shows where the posed bones are now relative to the new mesh. (Ignore the extra bones near his shoulders and hips which belong to invisible clothes. The Blend file omits them.)

Answer 1

If I understand correctly, you want to change your rest pose, but permanently, so that when you go into Edit Mode, the bone positions do not revert to any other position, because they've been truly changed from the position they were in originally, making the new position the new default rest pose, even in Edit Mode. There is a way to do this, and it's not difficult, but the steps are somewhat counter-intutive.

With your desired pose in place, go to Object Mode and select your character mesh. Go to the Modifiers tab in the Properties Panel, and locate your existing Armature modifier. Duplicate it. You may notice that the mesh jumps, but don't worry. For the moment, it's having the tweaks it's receiving from armature modifiers doubled because there are now two of them. Thankfully, this will be a very short-lived issue.

The next thing you want to do is apply the instance of these armature modifiers which is higher in the stack, and keep the other one.

Now go into Pose Mode and select all your bones. Press Ctrl + a and then from the Apply menu, select Apply Pose as Rest Pose.

You're done. When you go into Edit Mode, you will see that the armature really is in the new pose.

Hope this helps.