Nets:
Slow it down? What?
Nets should increase the distance which you can catch the moth, so you don't need to be on top of it to grab it. Unless of course you meant that it would be an item that would be thrown onto the moth... Come to think of it, that'd be awsome too. A throwing net to capture silk moths = awsomeness.
Bags/Straps: Between the shoes and backpack equipment slots on the paper doll, is a slot that only seems to be used by the quiver; that slot could be used for this when it's not used by said quiver!
* Bags could work like:
- Empty, the bag is 1-2 tiles large in the player's inventory. Objects are placed inside like Kilns are fueled (LMB select the item, then RMB on the bag)
- With 1 object inside, can NOT be placed inside the players' regular inventory; it can only be placed in the slot between the backpack/shoes, or on the ground.
- When it is on the ground, right clicking will cause a flower menu to appear with "Open" and "Equip" being the options available; one to open it like a normal ground-based container, the other to put it into the (not-being-used-by-a-quiver) bag slot.
- The bag has many horizontal tiles, possibly dependent on what the bag is made from, but only in 1 tile high rows; to stop weird things like buckets and arrows from fitting inside. (arrows would poke holes in the bag after all!

)
(?Clothing bags = 1 row of 10; Leather bags = 2 rows of 10?)- adventure->lift is possible (so the player can carry 1 bag on himself, and another over his head; at the normal crawl speed)
* Straps could work like:
Much more simple. If the object can fit inside a player inventory, the strap can carry it; but only that one object! +1 plank, or bucket, or quiver, or armor... Oh, and no infinite chains of straps carrying straps carrying straps; the object the strap is carrying is un-usable until it becomes "unstrapped" (like how the bag has to be dropped to be opened)
edit - forgot one of the suggested rules for the bag
The Dwarf is making a plaintive gesture. He doesn't really care about anything any more.