To my knowledge, you cannot store these items. To alleviate the burden of them filling your inventory, I suggest one of the following:

1) Go ahead and turn them in. None of them require more than 10 of the item (body seals) and the +2s don't take more than 6. So start finishing amounts and turning them in, get some of your gear. You CAN store the gear (Slip 09 for +1, Slip 10 for +2) to clear your inventory, so that way you both progress and clear out your inventory.

2) Get a same-account mule. It's not that expensive thankfully, since it's not a whole new dual-box, and you can send seals and +2 items to a same-account mule, which was how I alleviated some of my own clutter. My poor mule is loaded down with Hexed Abjurations, Limbus Chips, Empyrean weapon items, etc. XD

I personally prefer to finish things, as the majority of the mobs aren't too bad to farm up and kill. Some of them can be annoying, but for the most part with our iLvl gear, it's fairly easy to get these kills handled. And as I see you have DNC, it's probably even easier since you can be self-sufficient.