I considered tapcon screws, by the concrete was only about 3 weeks old, so i was a little nervous about cracking it. The construction adhesive seems to be holding pretty wellThere is no great way to do this one.
I'd bet just a sweep will not work, reason being from what I've seen in the past in old buildings like that is that slabs never level or flat, and the door most likely is not plumb.
As the door opens the sweep gets tighter and tighter.
If I had to do it I'd be using a threshold like this one.
https://www.homedepot.com/p/Frost-K...-Adjustable-Height-Threshold-DAT39H/100121731
When you get it, it's going to be to long, which is a good thing, you cut it to length (using a compound mitre saw going slow until you get through the rubber seal, any blade will work) open the door and use that sample cut off piece to set against the end of the door so you'll know how much will need to be cut off the door so it will make a tight seal, and also to mark that door stop molding where it will need to be cut to fit in the threshold.
It's best to remove the door when cutting, then it should be primed and painted after cutting or it's likely to rot.
Threshold should be set in a bed of silicone, to support the over hinging part outside I always use 1 X 4 vinyl lumber attached with TapCon screws pushed up tight in the slot under the threshold laying flat on the concrete.
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