Definitely seconding trying two point touch with your cane . Have you tried diferent cane tips? I find the small metal coated rubber ones in conjunction with two point tap do well with uneven sidewalks and narrow stairs. Adjusting your grip may help too. The open palm technique makes it so your cane can easily pop out of your hand if it hits something instead of jabbing you in the guts or chest.

There are different techniques for using mobility (white or green in some countries) canes in different conditions. It might be worth getting an Orientation and Mobility refresher course and addressing the specific needs in your area with the instructor.

The few times I have left my cane behind because I did not think I needed it something I did not see took me to the ground every time. At this point I cannot imagine leaving the house without Tap-Tap (my mobility cane). I no longer feel safe without it.

It even comes with me when hiking or backpacking. In those cases I usually have a walking staff or trek pole in my other hand

The 2 touch method works best for me in most cases. It seems to let me walk a bit faster and take longer strides. If I need to I can always slow down and switch to constant contact where I need more fine detail.

Most trekking poles have a rubber ferule on the end designed for gripping, so it might still get jammed. However, if you are mostly using it as a probe to check for depth and such, that could work.

For your white cane, have you tried two point touch instead of constant contact? That can help reduce it getting caught, but there is always a chance it would still.

I think this might be a less popular opinion, but for me, the high-mileage roller ball tip with constant contact works great on gravel and dirt and rough areas. I just keep a pretty light touch and use a longer cane so that the tip is at a lower angle to the ground.
When I do hiking poles, I use two, and generally use them the same way most sighted people do: alternating with right pole forward while right leg is back, left pole forward while left leg is back. I use them to catch myself with my arms if my feet stumble. If I need more input, I reach further forward with each pole step as I go and I use two point tap when needed. I definitely prefer using two poles for the reason of catching myself. The only issue is that people won’t know that you can’t see well so you don’t get some of the benefit of the cane where usually people will steer a bit more clear of you, or at least be more understanding if you make contact with them accidentally.

Additional suggestion: Along with two point touch, hold your cane with a pencil grip. Your intent is to probe the ground right in front of you, not 3 feet ahead.

Your situation is why I switched to a shorter, lighter cane and a ceramic tip. I can skim it above the surface and get an idea if the sidewalk is cracked/uneven without resting the tip where it can get caught. Not that it never happens, but it’s less. Another option is a Rover Wheel. Rolls over almost anything and if you use a pencil grip then the cane tilts up instead of jamming you in the gut since it’s on an axle.

No jab cane might be a good option with a dakota disk tip.

Edit: $1 and $1.