Just KISS approach… remember that the more factors you add higher are the chances of getting something wrong. It is important to clean everything but if your last steps aren’t “clean” then your done… all that care down the drain
If you have a pressure cooker, just use that. Put all your stuff above the water surface so it gets steamed. Once the temperature is right, 120° Celsius (if you splash some water on the lid and it evaporates quickly your good to go) count 30 min and the content is sterile.
However once you open the lid of the pressure cooker (unless you are inside a lab with controlled environment which is not the case ) all the nasty stuff will want to cling.
A trick for jars and lids for example is have them well washed with soap, then you put the lids on slightly screwed but not tightly. So that when the “cooking” has ended the interior of the jars is untouched. When you need to use the jar, you wipe it down with alcohol 75 proof before putting it inside the glove box. Close the glovebox and wipe everything down with alcohol again.
Soap will suffice to get rid of many bacteria and viruses by distroying their phospholipid layers in other words it kills most stuff, the problem is that it won’t kill those that sporulate or fungi, hence the Pressure Cooker method.
For tweezers, scalpels and all other materials you should do a flame sterilisation. Or high heat sterility by placing them inside craft paper and them placing in a hot oven for 2 hours at 170° Celsius, this last will ensure it is sterile until you compromise the packaging/craft paper.
It is the handling of the materials and your movements that will dictate the end results.
You mentioned that you rinse the jars with H2O but is it Pressure Cooked?
I’ll give you an example, in mycology there are many techniques used to make media viable for growing a certain mushroom or fungus. There are complex ways of doing so, there are also very simple ways.
Take this one for example. Sawdust pellets hot water and H202 and that’s it. It is very successful and simple way but there is a catch, the species is a very prolific one so it does not give time to others to take over.
I guess, and I don’t have any experience here, that tissue culture takes some time to develop. Maybe you should consider also buying media with some sort of antipathogen? An antibiotic? So in this case a selective media.
Hope this helps and is useful.
Have a look here just to get an idea of what I was rambling about
PS: I know your not growing mushrooms, but the principals aply