Fixing slope on concrete patio - grinding a drainage channel?

My house has a concrete patio (about 16×16 though its 5-sided) which is not sloped properly for drainage. In some sections it seems basically level, in others (near the doorway of course) it actually pools water.

The worst area I estimate slopes about 1/8" per foot the wrong way. I mapped it out by making puddles; this area is about 6-8′ across, sort of an oval. It, and the door, are in one corner of the patio. From the door to the yard is about 16′.

The concrete itself is in excellent condition. It doesn’t show any signs of settling nor is it cracked, I think it was just not poured with correct slope in the first place.

I am planning to deck this over with sleepers laid over the concrete. So the concrete appearance is not very important.

Ideas how to deal with the slope:

1. (CAN’T DO) Pour some leveling compound – height by the doorway is already very tight, can’t afford to lose any of it

2. (POSSIBLE) Grind channels to achieve at least 1/8" per 1′ slope, from the low spots to the yard. Rent a grinder like the example pasted below. Concern: might have to grind off a lot of material, maybe this is not practical.

3. (POSSIBLE) Cut channels with a diamond demo-type saw with correct slope. Cut as many as needed. Concern: thin channels may clog with time.

Are either #s 2 or 3 feasible? Am I missing anything important, or is there another option I’m ignorant of?