If you don't want to spend much, simply look for the AT92E(CD) - that's frequently offered for around 20 to 30 bucks in the US, so you should be able to find it pretty easily. And it's from the same cartridge family as the one you've already got, but with a better needle - just that that needle (ATN3472SE) alone typically is more expensive than the complete AT92E(CD). So with a new AT92E(CD) you'd practically get a spare body as well as a halfinch-mount adaptor for free...
Greetings from Munich!
Manfred / lini
P.S.: Oh, and the SL-DD22 is a pretty decent, slim direct-drive model. I.e., unless you'd consider yourself a demanding audiophile, it's not a bad choice at all.