In my experience dropping checks can help, as it shows a willing/grieving spirit. But you need to make sure that an elder knows you are doing it. If you approach the COBE (or elder assigned to you) that you would like to make a donation, but don't wish to make the accounts servant feel awkward, how do I do it? - Then if you give him a check for even say $5.00 he knows and the other elders will find out as well.
If I remember correctly from your other post, your with child. So if you have a elder that loves kids - stress you want to be reinstated before the baby comes out. You can't handle the guilt, etc. of giving birth in a bad condition. Ask them repeatedly (like a pest) what you need to do to make it right for your child. As you wish to "save" the child from the reproach. Or something like that.
Its all a mind game, just play it.