Don't fret mate!
My radio/TV background doesn't allow for much ripple on a DC power supply so I was expecting to see huge quantities of expensive smoothing capacitors on a linear supply of the sizes discussed here. For this application you don't need that much.

I'm not brainy enough to use Faraday's Law to work out the inrush for a given transformer, but I suspect you need a pretty chunky lump of iron for that to be the only significant contributor to the overall inrush.