A quick note on gem bonuses, and when they're worth getting.
For all intents and purposes, you can consider +8 Hit and +16 AP fairly equal. As such, you should generally put them in their respective colors. This means any socket bonus that does not require a blue gem is easily attainable. You'll need two blue gems for your meta as well, so you can fill out two blue slots with lesser DPS gems guilt free as well.
What about the third blue slot and beyond? Well, here's how I decide. We've already assumed that +16 AP and +8 hit are equal, so they'll be our baseline. So, by using a hybrid gem in a blue slot for the bonus, you're effectively cutting out 8 AP or 4 hit. So, let's say you have an item with a red and blue slot, with a +8 AP socket bonus. Putting in two 16 AP gems will give you 32 AP, but putting in a 16 AP gem and a +8 AP/6 Stam gem will give you 32 AP as well as 6 additional stamina. Thus, a hybrid gem is beneficial.
What if we had that same piece of gear but with two blue slots (like the BoDS), and the same +8 AP bonus. Putting in two 16 AP gems is still 32 AP, but putting in two hybrid gems gives us only 24 AP. For PvE, 8 AP is not worth the 12 stamina, so you can ignore the socket bonus completely.
So, what about the Belt of Deep Shadow itself? By using two hybrid gems you're trading effectively one gem's worth of stats for 3 agility, which is less than half a gem in return. Unless you need the blue gems for your meta, slap in the best Red or Yellow gem you can get and forget it even has a socket bonus.