Did you try blowing dwon the airline into it as I suggested (like trying to blow up a balloon)? This will tell you straight away whether the wand is blocked, or if you just need more air pressure, (which are the 2 most likely possibilities).
As for the air pump;
I can see your reasoning on that if you block one outlet all the air should come out the other, but they don't work like that. That would be correct if there really was just one pump and 2 outlets.
What you actually have is 2 bellows (like the old things for blowing fires), each with one outlet, all within one box.
As an overview you have an arm inside the 'box'.
When the arm moves left, it pushes air out of Bellow #1 through Outlet #1, and sucks air (from outside) into Bellow #2.
When the arm moves right, it pushes that air out of Bellow #2 through Outlet #2, and sucks air (from outside) into Bellow #1.
This is repeated many times a second,
(around 50 times if my brain is thinking straight) and this is what makes you seem to get constant air flow.
So when you block outlet #2, the arm moves left blowing air out of outlet #1, and sucking air into bellow #2. The air then tries to move right again, but bellow #2 is full of air and you have blocked the outlet, so it can't push the air out & therefore can't move very far. Because the arm can't move very far it means it doesn't suck much air into bellow #1, and then when it moves left again there isn't much to blow out.
Hopefully from that you can see how blocking on outlet actually reduces the airflow from the other one as well.
What you want really is one of these (available online or from your LFS)
You can then use some airline from each outlet to connect to each side of the T, and then run your airline (and checkvalve), from the center piece of the T to the tank.
Totally agree about your checkvalve, don't remove it, it's always better to have one, (in fact I use 2 because I am overly-cautious!), but if you do the above T-ing the outlets together, remember the checkvalve must be fitted to the pipe between the T and the tank, not between the T and one of the outlets, otherwise the other outlet will still allow back-syphoning
Let me know how you get on
