The 500/4.5 is certainly one of my favourite lenses... although the new price isn't as attractive as in the last year or two of the non-DG version, which saw it at £1995 or even lower.
I may be wrong, but if you put a DG teleconverter between a camera and a non DG lens, then you effectively get the (debatable) benefits of 'DG'. The thing to avoid is non-EX models of the 500/4.5 (and 800/5.6.)... EX makes a big difference and is what raised Sigma's profile in serious photography.

There's a mint Nikon non DG for £1399 at Surreyphotography.

Ultimately, a Nikon 400/2.8 (has to be AFS, the older ones were very slow focusing) would seem the best bet for action sports... but they are only a fraction smaller and lighter than my 600/4 and the 500/4.5 is tiny in comparison
See photo below.

btw: my 600/4 is currently on ebay if anyone fancies it.