How do I make my 'zs' and 'gy' sounds more natural?

I’ve been recording myself reading Hungarian news clips, but my 'gy' sound often leans too close to a 'd' and my 'zs' sounds a bit too sharp. It's frustrating because I can hear that I’m ‘foreign’ immediately when I say words like 'gyerek' or 'zsiráf'. I’m looking for tips on tongue placement or minimal pairs that I can practice to polish my accent for my next trip.