Ketones in urine

Hello all! I have a question regarding ketones in my urine. I've been on the keto diet for a month & have lost 20lb. I started checking my urine about a week and a half ago and I am consistently at 40mg/dL, moderate spill. I've been researching it and read that your body will eventually transition to not spilling ketones, at about a month in. Is now the point where I should see my strip decrease & what if it doesn't?  Should I be concerned if at two months I'm still spilling ketones?

The reason I ask is I worry about my uric acid level in my body.  Reseaching told me that your kidneys spill ketones because they think it's uric acid, but eventually learn, stop spilling ketones and start dumping urine acid again. But that means I'm still spilling ketones/ retaining my uric acid.  At two weeks into keto, for the past 2 weeks, I have had moderate swelling and pain in my hands when I wake in the morning.  I feel like it's a gouty type flare, maybe from uric acid buildup. That's speculation of course but I'm interested to see how I feel once I know the uric acid is leaving my body. Has anyone else had this? Does the discomfort improve over time?

PS please don't say "it's not Keto, it's arthritis". It was an acute onset of discomfort two weeks into keto, not a chronic buildup. I'm also young. Thanks!