New fixture old ceiling electric box

Trying to replace an old chandelier fixture. The wiring looks like this

The problem is the new fixture comes with a mounting plate that would be mounted to a regular box but its too big for this box and besides, there is no room for the wires and nuts to fit in the ceiling even if i would just screw the mounting plate into the drywall. the old fixture had the wires and nuts outside the fixture in a cover that went flush with the ceiling. What are my options with this? Thanks.

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So this is the new plate. The wire from the fixture which is not shown in the picture is supposed to feed through the center hole and then be connected above the plate with the connection in the ceiling. My friend had this idea of making a wider hole in this plate and feed the 2 electric wires from the ceiling down through the plate and wiring them to the fixture underneath the plate since there is no room for wires and nuts above the plate. My issue is the fixture has a dome cover that would hide the wires and nuts but it is a plastic cover. Is that an issue?