Intermediate plateau: how to sound more like a 'sabres' and less like a tourist?

I’ve hit a wall where I can understand 70% of Hebrew media, but my own speech feels stiff and formal. I know my grammar is technically correct, but native speakers in Tel Aviv know I'm a foreigner within three words. I think it’s the slang and the way they swallow the endings of certain words that I’m missing. How do you practice the regional 'Israeli' flow of speech without sounding like you're trying too hard?