Looking for advice on 'oü' vs 'ö' sounds

I’m prepping for a trip to Tallinn, and I'm really self-conscious about my vowel production. I keep getting corrected by the locals because I mispronounce the 'ö' and 'õ' sounds, which apparently changes the meaning of everything I say. Since I only have 20 minutes a day to practice, should I spend all that time on repetitive vocal drills, or is there a hack to make my current Estonian accent sound more 'local' without spending hours on phonetics?