Maybe I don't fully understand the "black screw" problem. When I reassembled mine I reattached the control panel assembly to the housing with all the screws, put the housing in place, pulled the control panel side of the housing out slightly and I was able to easily reach in and connect the two connectors to the board. Seems to me it would have been just as easy to do this in reverse. If I needed to do this again I would do everything the same up to the "remove the back" step in Chris Helming’s instructions, then, from here, instead of fighting with the black screws, I would:
1) Remove the one screw from the bottom of the toaster pointing up, and which holds the bottom of the control panel to the toaster chassis.
2) Detach the outer housing from the toaster chassis by gently (but firmly as it takes some force) pulling the outer housing of the toaster (plus the control panel which is attached to it) backwards, but only until it disengages from the chassis - the control panel is still connected to the toaster via ribbon and power cables!
3) You should now be able to pull the control panel side of the housing outward and be able to reach in to disconnect the two connectors which go from the control panel to the board on the toaster.
4) With the connectors disconnected, the housing + control panel can be easily removed from the rest of the toaster.
5) Now, with the housing off the toaster, you can then easily access and remove all the black screws which attach the control panel to the housing, disassemble the control panel, work on the board, etc, then reassemble in reverse order.