Ok, firstly, you are making the common mistake of confusing Angle off the Horizon with Angle of Attack. Angle off the Horizon, in this case about 15° you say, is merely a convenient reference to a fixed feature in the plane's environment...the horizon. You seem to have the nose 15° above that. All well and good, but totally irrelevant in this case. The STALL warning works off the ANGLE OF ATTACK. This is the angle at which the relative wind, or the wind the aircraft sees as it plows through the air strikes the wing.


As you can see, the slower you go, the more you pull up on the nose to maintain you climb angle, but this increases you angle of attack. You can have an increasing angle of attack with a constant
pitch as shown in the second pic, above. Just need to slow down a triffle.
YOUR problem, as I see it, isn't the angle above the horizon, 15°, but in your case, your SPEED is too slow for the action you want to accomplish, in this case climbing at a certain VS, or Vertical Speed. Only one thing to do to solve the problem:
SPEED UP! 
This will lower your AOA (Angle of Attack), thus removing the stall warning, which sounds to let you know the
relative wind is getting ready to separate from the top of your wings, as shown in Figure 2. This happens, no lift, No lift, no fly, and you fall down and go BOOM!!

Hope that helps out a little bit

Pat☺