Then you need better quality axle nuts and probably need to work on your technique for mounting your wheel and setting chain tension. I’m not saying ditch the chaintugs, but that’s not their purpose. I understand exactly what you’re talking about in fitting larger tires. I actually run a 70s era converted road frame with 32mm tires myself, but you shouldn’t need any chaintugs to help keep an axle in place. Also, I personally find forward dropouts easier for everyday use than track style fork ends, but to each their own.

one thing you could use are traditional drop out screws that thread into the back face of the dropout. I’m sure your frame has threaded holes for them. You can buy new screws from Velo Orange. The type that would have been originally used on your bike, for quickly setting wheel position. That’s what I use on my bike and it makes setting my wheel very quick and easy.