Instead of trying to make an axle and make sure it's centered, I figured I just create my own bearing by putting balls between two wooden surfaces and supporting it at 3 points around the circumference to restrict its movement on the XY plane to a circular one.
So I was looking for bearing balls to make this big bearing, and I figured that it is not economical to order 200 pieces of 15mm balls through Aliexpress because balls are heavy. Probably steel isn't much cheaper in China either. So I found a company in this very same city Wien which sells all kings of spherical things, and they sell "polishing quality" steel balls for 8 € per kilo. I estimated that I need about one kilo of 15 mm balls in order to get a single line of balls around the 600 mm diameter table.
When I was in the shop, it turned out that they charge you 10 € extra for any orders below 50 €. So instead of getting 2 kilo of steel balls, I bought 6 kilo - I didn't wanted to pay this handling fee. I bought 5.56mm, 12.7mm and 15mm diameter steel balls, 2 kilo each, so I now have about 3000 pieces, give or take a few hundred.