I find that using a tripod 'monopod stand base' helps with that. Here's the one I use: https://www.amazon.co.uk/Koolehaoda-Monopod-Monopods-Ballhead-KM3/dp/B07W45K2WD. In addition, the extra grip & stability greatly increases the number of places where a Stick can safely be left just leaned against something.

Perhaps another factor in why I don't have the problem is that in my custom design I had getting the point of support close to the line of gravity of the Stick as a design aim. The point where my base touches the floor is close to being in line with the beam of the Stick (if the Stick is held vertical, the base is directly below the thicker part of the Stick). That means that the Stick has little if any inclination to swing round to a more gravitationally stable position.

Here's a list of the parts I used. The Brands are Niceyrig, Camvate, Smallrig. I think they are all HK based and may sell also on Ebay or similar sites. There are many similar systems and parts, and most are compatible. You just have to pay attention to the thread dimensions.

https://www.amazon.co.uk/NICEYRIG-Switching-Camera-Railblocks-Dovetails/dp/B0799KHNS6
https://www.amazon.co.uk/CAMVATE-Rosette-Standard-Connecting-Adapter/dp/B07P7PZD3N
https://www.amazon.co.uk/NICEYRIG-15mm-Clamp-Rosette-Mount/dp/B08YQPCZSB
https://www.amazon.co.uk/SMALLRIG-Extendable-Aluminum-Support-Camera/dp/B0093XN9XU?crid=1M6EBG6LQA1P7

The rubber part is from nordic walking poles and can be purchased at a sporting goods store. It's important that the inner diameter is 15 mm, otherwise the rubber won't fit.

Great idea, David! I tried it with a small microphone stand, but it was too flimsy. But the monopod stand in your link should work.

Thank you. I already have some SmallRig bits for my webcam setup, so I wondered if that brand might come into the equation.

I like the look of that mounting plate as an alternative to the DIY cut & drilled wooden based I already use, & that M6 Connecting Mount would match the thumbscrews I already use to attach the dismountable parts.

An alternative would be to switch to thumbscrews that matched a suitable hole in the plate, but I see more attractions in the Connecting Mount.

I don't have any issues with the monopod unintentionally rotating.
The rubber foot and my two thumbs keep it from spinning.

Your monopod looks offset to one side.
Mine runs on the centerline.

Sorry, I didn't center it for the photo. However, the rosette clamp rotates easily and clicks into place every 6 degrees.

yeah it is adjustable and it looks like it comes off - you could ask at https://thinkns.com/technical-support/

NXT stand open box:
https://www.sweetwater.com/store/detail/NXTDBTS--ns-design-nxt-double-bass-tripod-stand?cond=NXTDBTSd1