I'm not sure about synthetic, but with down I would guess 30L with all that gear. With synthetic, maybe 40L? But it also depends on the type of hammock and tarp you have. My Warbonnet Blackbird is twice the size of some other simple hammocks I have.
So 40L plus a jacket, cook kit, maybe a down or fleece mid layer...you could be around 50-60L.
There are really too many variables though. You'll want to try them in person and consider:
1. Comfort is always number 1. If the pack doesn't feel comfortable and fit your body well, it doesn't matter if the pack itself is 1lb or 5lbs. And of course it will only get worse as you add more weight.
2. How you pack it. On some trips I feel like my 25lb load is 20lb. Other times the 25lb load feels like 35lbs. I'm never exactly sure why, but it probably has to do with the center of gravity, items shifting, down in the bottom not compressed enough/too much
3. Don't overfill a 40L pack; don't underfill a 70L pack. I found it is always more comfortable to fill a pack so there's no/little extra room without struggling. While my 65L pack was always comfortable, I ended up buying a 50L in the exact same model since it carried better than the under-filled 65L pack. Compression straps can only do so much on packs.
4. Instead of going to a store, buy and try at home from any seller that allows returns. It's well worth the $8 to return; some are even free! (Zappos, Amazon, etc). That way you can take your time packing actual gear at home, walking around, up/down stairs, whatever.
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