I have spent years working in cramped setups, and honestly, that 90mm is a total beast but it is probably gonna fail you in a small Chicago studio. You need a lot of working distance just for a basic headshot with that thing. If you want half-body shots, you will literally be backing through the drywall. In my experience, you should look at these three for your studio:

• Fujifilm Fujinon XF 56mm f/1.2 R WR is the professional choice for small rooms. The newer WR version is much sharper than the old one and the autofocus is way more reliable for client work. It gives you that classic 85mm look without needing a football field to stand in.
• Fujifilm Fujinon XF 90mm f/2 R LM WR is arguably the sharpest piece of glass Fuji makes. Bokeh is smoother than the 56mm because of the compression, but in a tight studio, you are limited to tight headshots only. If you dont have 20 feet of depth, forget it.
• Viltrox 75mm f/1.2 AF Fuji X-Mount is the one to get if you want to save cash for lights. It sits right in the middle. It's built like a tank and the image quality is actually insane for the price. It's basically a pro lens for half the cost. Since you are on a deadline and have a tight space, just grab the 56mm. It is the most versatile lens for pro work when space is a premium and it fits your budget perfectly.

Been thinking bout your setup... back when I started in a tiny basement, I realized depth's everything. How many feet of clearance do you actually have from the backdrop to your tripod?

• Sigma 56mm f/1.4 DC DN Contemporary: AF stepping motor is snappy. Fast. Reliable. Tho it lacks weather sealing which is a risk.
• Tamron 17-70mm f/2.8 Di III-A VC RXD: The 5.7-stop VC is way more reliable for handheld work.

Been using this for years, no complaints