Hello, welcome to the best lucid dreaming site on the net!!
First off, know that you do not need sleep paralysis to enter a dream. Your goal should
not be to enter sleep paralysis, but to enter the dream itself.
You left out a very important step in completing a successful WILD:
It's called Wake Back to Bed or WBTB. The reason you need to do this is that in the beginning of the night, your dreams are about 90 minutes apart. Your dreams during this time period are also of significantly lower quality than those of later hours of sleep.
What you need to do before you attempt a WILD is to sleep normally for some time and then stay awake for some time. I have had the most success sleeping for either 4 or 6 hours and staying awake for 1 hour.
So you sleep for 4-6 hours to get your REM cycle (where most dreaming occurs) to become much closer together, like around 15 minutes apart. Then you wake up, via alarm clock, natural light, bathroom break, anything. Now you stay up. Staying up greatly increases that chance that you will not drift unconscious while waiting for the dream to form.
Although concentrating on breathing may work for you, I would suggest trying other things. I find that concentrating on something as simple as breathing is too dull. Perhaps you would have better luck thinking about what you will do if your WILD attempt is successful. Doing this will also save precious lucid time since you won't have to think about what to do. This will also increase the chances of a DILD since you are thinking about lucid dreaming (right before falling asleep).
I don't know why you don't go through sleep paralysis, but it is not uncommon for a WILDer to miss out on sleep paralysis. I have never experienced sleep paralysis. I think that when people experience sleep paralysis, it is usually when they wake up from a dream prematurely.
Depending on whether or not you are using WBTB, you may be close to a dream. If you sleep for 6 hours before attempting a WILD, you should only be laying down for 15 or 20 minutes (at most) to enter a dream. I'm not too sure about this, but this has been my experience.
Also, if you haven't already, check out the WILD and WBTB tutorials on the site.
Feel free to ask questions and once again,

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