Dealing with Waswasa During Istinja

I realized my waswasa had become severe when I woke up for Fajr with only 27 minutes until sunrise. I could have made wudu and prayed, but I knew from experience that it might take 5-15 minutes or even longer for the urine drops to stop, so I just gave up and missed Fajr, praying later after a shower. And indeed, it took even longer when I finally went. Even when I use toilet paper along with water, drops remain at the tip without falling, and I can see them on the seat, especially after waking up. How can I stop these drops? I've read online that squeezing the private part is a bid'ah and medically unsafe, and that one should wait 30 seconds to a minute for drops to stop naturally by gravity. For me, it takes much longer. Before I knew the rulings, I would wash and get up immediately, possibly praying with impurity and invalid wudu. I might have done that for thousands of prayers. But even that instant getting up was less of a struggle than what I face now. Alhamdulillah, I seek Allah's help in overcoming this trial.