Seal Old Chestnut Door?

I have beautiful old Varnished Chestnut exterior door (40" wide) and am looking for ideas to seal the Door bottom.There is roughly an 1/8" gap between the bottom of the door and the threshold (also chestnut). I really dont want to replace the 40" threshold if it is avoidable. The rest of the door has been upgraded with insulated glass and compression weatherstripping on the outside frame. I just need to fill the bottom gap. It is under a porch roof so a drip edge isn't important. I have already explored standard sweeps but the door overhangs the tapered part of the threshold by about a 1/4" inside and out. Since the compression weatherstrip is on the outside, sealing the inside will leave an air path at the bottom. I had one idea but don't know if it even exists. Is there anything out there that would fit into a groove routered out of the bottom of the door? I seached the web to no avail.

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