Might need a script on the SO_InvoiceHeader to loop through the lines on the pre-write and if all lines are backordered, remove the miscellaneous charge item from the invoice, not the sales order, this should keep the charge item on the sales order even when the sales journal register is updated.

I think you might have to change the charge amount to zero (instead of removing the line) so the SO is updated properly during posting.

Probably best to test through the UI before writing the script. I think as long as the charge line is on the invoice, regardless of amount, it will be processed and removed from the sales order during posting but i'm not 100% positive of this. Test with whichever entry task (Shipping Data Entry vs Invoice Data Entry) that will let you delete the charge line or change the charge amount and post it and see what happens. 

Indeed.  Something to test.  We know that if a Miscellaneous item is not on the invoice, the BO quantity is not updated on the SO when the invoice is posted, but I am not sure how charge lines work.

So I tested both Shipping Data Entry and Invoice Data Entry. I removed the charge line and updated. The line was no longer on the back ordered order. I don't think this will work for us at it stands. I think that I would have to add a script to the invoice header to remove the charge line and edit my existing script to add the charge line to backorders where the criteria is met. Why can't there just be an option to ignore charge items if there is no product being invoiced?

Did you also try just changing the charge amount to zero?

Looking at this another way, does the charge item have to be on the sales order for any reason, such as customer facing docs?

If not, what if you instead moved the script to the invoice header so the charge line is only added when no lines are backordered (might need to think through any scenarios where this could be a bad thing)?

EDIT: 

Worse case scenario, add the script to remove the charge line from the invoice if the criteria is met and you modify your existing script as you said to make sure the charge item is on the sales order. May need to also have it check history to make sure it wasn't previously charged in the event you have all all but one line shipped, wouldn't want the charge line added more than once.

Why post the invoice when nothing is shipped?  That is not normal.

As it is right now the Charge item is a Small Order Fee that is a 15$ charge on orders under 100$. Unfortunately I cannot change the charge dollar amt. 

What would be a better way to do it then?

Maybe to change the order type to backordered for their process/reporting needs?