The reagent limit does not represent the reagents you're lacking, it represents any reagent that may be 999 or over.
Common reagents that are often like this includes:
Mist Wood Stoneblocks Golden Pearls Pearls Sandstones.
So, do another quick sweep of your bagpack (particularly the reagent tab) and check each reagent you may have and see if any are close within the 999 proximity.
Packs have different items in them and each of the 7 items is a roll on the drop table. If an item is avaiable as a drop we can not open the pack unless we have 7 spaces for that item just in case we get 7 duplicates. I've never heard of anyone getting 7 duplicates and I suspect there is something in place to prevent is but we must have space for it so we can not possibly lose any item we have bought/won/been gifted.
Go to your reagents and double which ones are above 990 and pop a few into the shared bank or sell them so you can open your presents
I hope you get really cool things from your packs! Good luck!