Doors and Windows - steel entry doors with panes on the outside

I have recently purchased a home with double steel entry doors. The only draw back is that the panes are on the outside of the glass on the interior and exterior. This makes cleaning the glass impossible as the cleaner runs in behind the panes and down the next pane. Has anyone ever cut the panes out? I have checked out replacing the moulding but am told that I would need to replace the glass as well. Apparently it is sold as a unit, at 3/4 the full price of replacing the doors. Any ideas would be welcome.

Might try spraying the cleaner ON YOUR CLEANING CLOTH instead of directly on the window. Shouldn't run.

Thanks for the reply, but I have tried that and it is still an inconvience. I have even tried to remove that moulding but it holds the window in place. I am considering trying to exacto the panes off and leaving the moulding but I am unsure as to what to use to fill the holes.