That's the reason why I use an undersized .41 caliber jag in my larger caliber guns.
It's really pretty narrow, but I compensate for that by cutting large homemade patches and fold them over enough times to get a really tight fit. They'retight yetthey stillhavea little give sonot to getstuck very often.

My cleaning rod has a handle on it like yours, but I also have a device thatwill griparamrod with leather paddedjawsjust in case aplain smoothramrod gets stuck.

Some folks turn their jag down a few thousandths of an inchto better accomodate the thickness of their patches, especiallywhen the bore is fouled.