Driveway pitch water in garage. How to mitigate -- best of two solutions need quick response

Water is backing up under the garage door slightly. The pitch is essentially level outside the door (not pitching away). Water builds up during rain and comes under.
Regrading/repaving the driveway is out.
I have thought of two solutions. Which one do you guys think is the best.
Install a saddle for the door to sit on. Cement it down with Liquid Nails to provide a waterproof seal. This will not remove a small (1/4") amount of water against garage trim during the rain, but might keep the garage inside dry.
Cut the cement apron of garage threshold across the width of the door and put in a metal drain. I have a sump pump right inside the door. Could drop a pipe to it through the a slot in the slab (and recement over pipe). This willl drain the water from the garage threshold area to the sump.
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