Solving stuff in other stuff can be exhausting. I first discovered this problem when making the PVA slime. The pva-flakes did not dissolve completely when stirred by hand. So i looked up magnetic stirrers on eBay and immediately decided to go for plan B: build one myself.
I previously had bought some strong neodymium magnets and just needed something rotating to attach them to. The first thing i found was an old 8cm fan. I had concerns on wether the magnets would interfere with normal motor operation, but they proved to be needless.
To magnets were glued on top of the rotor with opposite poles facing upwards. I used double-sided adhesive tape and superglue and another layer of tape on top.
For the stirrer itself i used a small cylindrical magnet. To protect it from aggressive solutions i stuck it in PVC tube and sealed the ends by melting the pvc.
Then i tested wich distance from the rotor was best to achieve good rotation of the stirrer and place a piece of plexiglass over the rotor in that height. (Fortunately i had screws that fit perfectly).
As you can see in the picture, it worked quite well.
If you want heating too, you can just place a peltier-element between the stirrer and jar.