Are there any light mounting products that is adjustable?

One option for front lights would be to replace them with torches and rubber/velcro mounts such as below, these would be interchangeable and fit pretty much anything - I have even got my iPhone on to one.

As for rear lights you may have to invest in 3 sets of the same light. alternatively in the past I have had to DIY mounts using elastic bands in emergency (not long term solution).

Otherwise consider carrying the lights with you! in the long run it's probably more sensible to have one set that you can keep track of battery wise and condition wise.

If you only use the lights rarely, then you could leave a roll of electrical tape at each location. You can take the light mountings off your bikes. If you need a light tape it on, and afterwards throw away the bit of tape you used.

For front lights tape over the light and under the bar, and back up over the light crossing the first taping at 90 degrees, and go under the bar again. For back light it might be trickier as depending on the design, tape may end up going over the lens.

Anyway, you'll have to make the judgement as to whether this is suitable as a cheap solution. If you want something more permanent, perhaps buying a matching lights would be the best way.

I use hardware store bought flashlights mounted on my handlebars using hose clamps. I'ts as generic as you can get.

I use a strip of old inner tube to protect both the flashlight and the handlebar. That also increases grip so the light is more stable. It's not as fast to install as a commercially available solution, but takes no longer than a minute. Gluing the rubber strip or a small piece of foam tape to the inner side of the hose clamp can speed things up.

This mounting is fairly substantial and it even holds up to MTB riding on rocky trails.

I select the flashlights that have similar beam patterns and functions as a proper bike light, like light intensity levels and/or blinking (I suspect the components are effectively the same, the bike specific ones just use a special housing and change the price accordingly)

If your existing lights are mostly cylindrical, you can use this approach. Use foam tape or rubber strips to cushion the lights. You'd need two clamps per light. One goes "permanently" affixed to the light, with the second clamp interlocked like a chain link. The second clamp goes to the handlebar, and this is the one you open and close to install or remove. (So you leave the bike clean when not using the light)

A more elegant solution may be to 3D print adapters or mounts that can work with many of your existing lights. Or, you could make copies of some of your existing light mounts and have many mounts on one handlebar. I'd go with this approach if the existing lights where particularly good but also expensive enough that I'd not want to spend on.

But, ultimately, most lights use mounts that are fairly easy to install or remove with no tools or at most using a simple screwdriver (something that you should have always at hand when riding bikes, in a multi tool or small tool pouch).

For example, my wife has one where the mount is a special molded piece covered in rubber. The solid part half wraps around the handlebar and a thick rubber "cord" wraps the rest and locks into a hook in the same mount. It can be removed or installed in just seconds. The mount is semi permanently attached to the light's housing and allows for side to side angle adjustment.

I borrowed this light on a short period in which "I did not know beforehand which bike I'd be riding". I just carried that light in my backpack and only installed if necessary