Am I missing a simpler process/formula/VB solution for this?
I think what could be happening is that the format for the cell with
the formula is set for general. When it displays the text of the
result, it looks okay, but it's just text. Maybe try setting the
format to an h:mm:ss format and use this formula:
=IF(ISNONTEXT(B1),B1,IF(LEFT(B1,1)=":",TIMEVALUE(" 0"&B1),B1))

So we get those numbers fixed. *Now in my example I can take A1 and
subtract B1. *I can also subtract C1 because it is already in a
compatible format. *D1 on the other hand is in General format and even
when I try changing the format manually to [h]:mm:ss I cannot subtract
it from A1. *I do not understand why it will not work.

Any thoughts here?
Try using the =Timevalue(D1) function.