Had been locked up for almost two days when, this morning, I had a testicle manage to finagle its way free.... then, a little later, the other testicle made its break for freedom as well and I had been uncaged.... I showed my wife the empty cage and she asked if I freed myself... so I explained what had happened... her comment was "Well.. you can be free until after Thanksgiving, then..."
Your ring is too big... I had a similar problem myself after I ordered a steel Keyholder's Prize cage. I didn't know my correct ring size at the time and it was very easy to slip out of it. I ordered another with the correct ring size a few days ago and I'm just waiting for it to arrive. If you put on your ring and soap/lube up a finger, you should be able to get your finger between the ring and your balls up to the first knuckle, but no further. It should be snug but not too tight. If you can get a whole finger through, then the ring may be too big. If you get 2 fingers in then the ring is definitely too big. I asked a similar question to this on another thread here and they explained it in detail. https://www.chastitymansion.com/forums/index.php?threads/a-kinky-perhaps-dumb-question.53584/
I'm pretty sure that the base ring is snug enough. I think it more to do with the gap between the base and 1st ring of the cage part... the gap area to which you alluded...
I occasionally lose the smaller of my two. Most likely to happen when I've been out in the cold, got high and tight, and then sit down. I'm on a 55mm base ring. I've got a 50mm, but get a severe burning that no amount of lube or adjusting can relieve. Like OP, I need a bigger base on the top ring to reduce the ball gap. Or a bigger ball. Hmmmn. That's got me thinking. I'm on TRT and they're getting smaller. What if they get to the point where an orchiectomy might be needed? Could I specify a nice chunky pair of prosthetic nuts? The only things my current ones are good for is to anchor the cage and allow my Goddess to indulge in some ball busting. They don't make testosterone anymore, and I've had all the kids I'll ever have. I'll admit I'd miss the busting if they were replaced with falsies.