Best way to finish outside basement door

Hello. This was hard for me to describe in the subject line, and I apologize up front for the long post. We have a sliding glass walk-out basement door. When you walk out, you're pretty much right at ground level. The thing is the house is on a slope; all grading works really well for water to run away/down from the house. The only tricky part is outside that basement door. It's at the bottom of the slope, right at the end of the house. Most yard drainage water goes right past the door and down and out toward the street, but a small amount gets "lost" and takes a left turn, and heads toward my basement door.
There's a "pit" for some reason right outside the basement door. The "lost" water above pours into this pit and fills up--if it's a torrential downpour, it fills up and spills/seeps through the bottom of the basement door threshold/casing (it's aluminum) into my basement. This "pit" is about as wide as the doorway (5 feet or so) and extends out about 3 feet from the quite a little pool can form. The house's previous owner (we've been there just over a year) put a wooden "bridge" over this area and I didn't see the pit. The "bridge" lets you walk out from the door onto the wood, rather than right onto the grass/yard.
I figure I have a couple of options to fix. The best way, I think, would be to fill the pit with fill dirt, packing it real tight, and hopefully sloping it slightly away from the basement door--if I can do that right, the overall yard rain runoff would simply keep going down past the house, and not taking the left turn going toward the "pit". In other words, filling in the pit would keep that area from being the low point. I _think_ this should work. The only problem with this is that I wouldn't really be able to put the wooden "bridge" back on top of the pit area: it'd be too high--you'd have to step up onto the bridge when you walk out the door--not good.
On the other hand, since it's a walk-out basement door, couldn't I have some sort of concrete slab-type area right outside the threshold, about the same size as the "pit"? Rather than walking right out the door onto grass/dirt/whatever? If I dug out a nice rectangular space (and dug it down another foot or two??), could I just put some plywood forms in there, pour in concrete and have a nice slab onto which I can walk? And would a concrete slab help keep some yard runoff from heading toward the basement door?
I'm thinking if I have a basement/drainage outfit come out and look they'll want to install a drain right outside the door, put in the concrete slab, and run the drain into a second sump pump that they'd want to install right inside the door (I already have a working sump pump on the opposite end of the basement: the end that's mostly underground). Then pump the sump water out where it belongs. I'd like to avoid this since the overall sloping/grading of my yard looks like it should allow for "natural" draining. I'm just not sure the drain thing would be necessary.
One more thing: my roof drainage is pretty nice: all the gutters drain into the ground, and all these drainage pipes go down to the storm drain out at the street. Can't remember what that type of system is called, but it seems to work well. If I installed a drain outside my basement door (which would catch excess yard runoff water), could I have that drain tap into the roof drainage pipe system? Does this question even make sense?
Again, sorry this was so long. Thanks for any ideas/thoughts anyone has.

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