Hello, here is few ideas how to make straw storage a bit less carts inside stables.
1) Static straw storage 2x2 tiles, something like large haystack covered with cloth. 6k storage wheat straw only. Farming or advanced farming, made with simple cloth, simple rope and branches.
2) Strawroll thingy, slightly larger than barrel, movable like furniture, made with 200 straw and 1 simple rope Farming 60, disassembled back into 200 straw. Can be put into horse cart slots like logs.
3) Horse cart customization, increasing storage but limiting to specific item types.