I'm looking at a handlebar that is 90mm reach vs. 75mm on my current one. To replicate my current riding position can I use the new handlebar with a shorter stem or is there more to it than that?

Same shifters? Same width? Same drop?

On paper, yes you can. In real life mostly yes, very rarely no.

You're keeping the shifters in the same place but moving the tops and sometimes the drops. This is usually not an issue but I see the occasional fit where the bar height needs to go up/down to get back to a comfortable position.

Yes, it depends upon how much time you spend on the tops which wouldn't change with the shorter reach bars. Also, depending upon shape/curvature and angle of the new bars, the lever hoods could end up closer or further away than you expect. In my case I ride the hoods most of the time. I would record the reach from the saddle tip to the apex of the lever hoods then install the new bars, and measure again. I would work to get the measurements the same by sliding the levers up or down the curve of the bars and/or tilting the angle of the drops within limits of practicality. Only then would I determine whether a new stem were required.

Play around with the stem calculator, it may not be as simple as getting a shorter stem with the same angle.
Stem Comparison Tool | yojimg.net