Copying and pasting a Photoshop image into Illustrator can achieve the correct size.

Hello,
I have read more than 20 posts about Illustrator's incompetence when importing raster images, yet I still cannot fix it.
A blueprint needs to be traced to scale in Illustrator. Using Photoshop, I resize the blueprint to 1mm per inch. Using Illustrator with the Photoshop Image locked behind it, I trace the blueprint with the same scale. It appears as some random height and width every time I cut and paste it. Every explanation that claims Illustrator only sees images as 1/72" or 24% of the original at 300dpi has been read.
There's no way I'm going to listen to another ridiculous explanation about why Illustrator doesn't make this super easy. If they need to make it a special feature, they should. But knowing how little they care about useful updates, I am willing to compensate if someone can just tell me what to do.
Assume that I have a 3000x3000 px document in Illustrator with rendering intent set to 300dpi
In Photoshop I have an 800x800 px document (at 300dpi)
When I paste the image into Illustrator, [hidden link disabled by Moderator] it should have 900px X 900px dimensions.
As long as I can accurately import an 900x900 (300dpi) image that I can rely on for tracing, I don't care about Photoshop steps.
Despite reading and reading, I am unable to find an explanation for this. Illustrator should have this built in as a simple, simple task. I apologize for sounding so grumpy, but seriously, I don't understand why anyone would do this. I appreciate you explaining this in advance.

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