Hardwood floor too high for door

by Jim
(Schodack, NY)

Hello,

I recently installed 3/4" hardwood floor boards throughout the house.

Prior to installing the hardwood flooring I installed sheets of 3/8" plywood over the sub-floor because my sub-floor is OSB.
I figured the staples securing the hardwood would hold better like this.

When installing the flooring, I left a landing area by the exterior door in order to install tiles or vinyl that would handle the outside elements better.

To bring the landing area level with the flooring I will have to build it up 1 1/8".(plywood-3/8" + hardwood-3/4")

My problem is when I raise the landing area I'm not sure the door will be able to open without hitting the floor and I don't know how to finish it at the threshold/floor meeting point.

I'm pretty sure I'm now supposed to run the new flooring under the threshold. I can't anyway because there isn't enough space between the top of the door frame and the header.

My exterior door is metal and I wouldn't be able to cut it.

I don't know what to do. It's been like this for a few years while I worked on other projects.

My basement door and exterior door in the kitchen are going to have the same problem.

Hopefully I presented this question clearly, thanks for any help.

Jim
(Schodack, NY)