It looks well made. A ruler will not be accurate enough. Do you have a 3mm drill bit for example?
What you need to do is find something 3mm thick (exactly, not approximately) and put it between the plates to measure the spacing. A metal shim is good for this. If it is not 3mm then you need to make it 3mm by resoldering the patch with a blowtorch or hot air gun. If you use a damp cloth behind you can prevent the reflector and connector from unsoldering while you melt the solder on the patch.
Some people found a slightly under 3mm (say 2.9mm) aluminium shim between the plates is a good way to get a 3mm spacing. The difference allows for it not being easy to ensure it is tightly compressed together when at 350c. When that's done you should have a good match but if not it is possible to adjust be very slightly bending the patch. However you really need to have access test equipment to do this. They are only $60 for a Nanovna working to 3 GHz, but I recognise that unlike in the UK, you can buy a lot of beer for $60 in OM, so perhaps the local radio club has something they can lend?