Tricky situation pal, but not the worst, you have a job in hand and potentially another. Seemingly if you have reached out and they haven't said no it means they havent reached your file or are still deciding.
That being said, take the one you have, the EI process is known to be drawn out. Some people get the good news several months after, rumors tell of one person hearing the good news after almost a year!
Take the offer you have and deal with the EI opportunity when and if it comes up. I know this comes with bonds and other complications, but what else can you do? I've heard they aim to send offers and rejections in about 4 week's time, maybe you can stall the other one somehow.