I like the idea of item slots that limit inventory... but feel your implementation is a bit over-complicated for my tastes. At least, over-complicated as far as gaining additional slots for Str, and having weapons or armor take up multiple slots.

You have slots for a Rucksack, Satchel, Bags and wearable slots. While carrying your Rucksack you are Encumbered and have Disadvantage on Athletics and Acrobatics. Characters are space limited and don't care about their Str for inventory purposes, this forces tough decisions and really captures the traveling light idea.

I designed an inventory system for my RPG that should fit the bill well enough. Essentially you break carry-able items down into Small(S), Medium(M), and Large(L) categories, occasionally items like carried(not worn) armor or particularly large items will be 2xL or 3xL. Two smaller sizes can be stored in the larger size, not visa versa. Some items like arrows and javelins etc are grouped together, having potentially a different size for their single item and their pack.

A character has a Rucksack(4L, 8M, 10S), a Satchel(2M, 6S), two pouches(4S), and two Misc(M) slots. They also have slots specifically for four weapons, 2xL, 1xM, 1xS slot sizes. They also have one Shield Slot and one Armor slot whether or not the use them.

Now, some of the Rucksack is automatically filled, essentially with a basic adventurers kit. It's assumed the character replenishes their pack back up to this point whenever convenient. Also, while wearing a Rucksack, characters are automatically encumbered and suffer Disadvantage on their Athletics and Acrobatics checks. Characters do not want to go into battle with their packs on. So, once adventuring characters are stuck with their wearable, their Satchel, 2 Bags, 2 Miss, and weapons and armor, they'll be quick to be very selective with what they take out of a dungeon.

What is nice is that the character has these spaces laid out visually and all they have to do is fill in the corresponding blanks. And man, see how long characters try and adventure with their Rucksacks before they realize they need to leave them behind with the horses and travel light. There is no need to track weight or encumbrance etc. If a character tries to carry something more, ask them "How?", and if they can't in their pack etc situation, they have to carry it in their hands and could pose it's own problems for them.