I think you should be able to see fringes with that setup – one fringe from a green LASER is about 0.25µm (0.00025mm) deviation.
You could probably find a piece of window glass that is quite flat if you had enough pieces (3+) to compare against each other using interference fringes.
I would encourage you to keep going, as it is possible – this is a small (~30mm x 50mm) octagonal flat that I made for a Newtonian telescope a long time ago. The fringes are from a neon lamp, so are about 0.3µm.
(Apologies for the image quality, but they are cropped from larger images, captured at low light at a time when 1.3 megapixels was the cutting edge of digital photography!)
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Good luck!