An easier fix, that would be more in line with how druid is supposed to function in 5e would be to disable inventory completely while shifted and treat it as if you had an empty inventory, as when a druid shapeshifts the items they have on their person fuses into their new form and becomes a part of them until they return to normal.
Seems an ez solution, but its not gamewise. As you allready read, some people have to play inventory shuffle because of the low strength at Cat. So i you going to be realistic as in 5E Rules and items are fused into characterform, then you are true to rules but one more step to itemshuffle. Even more so i say you are limiting yourself in what items that druid is carrying at all times in his inventory to not start itemshuffle beforehand, meaning before you change into Animalforms.
Thereby, a good compromise is giving animal form a free to go inventory without limiting to a n animalform but give animal the Druids STR Attribute and having more fun in the game. But Attacks should not be bound to STR of Humanoid form and be like a special attack, just for the sake of having fun in game and not restrict the flow of the game. So a cats attack is weaker then a bears form.
The inventory managment is allready a big task and slows down everything. So dont make it much worse.
A game needs to have more pieces of fun then beeing totally true to some rules. Then it will tread the golden path of the middle, whatever...