I'm supposed to have the heart key at this point? I have the turquoise one you get first, the green clover key and the spade key. The only one I'm missing is the heart key which is the last of the 4.
I looked it up and it looks like I missed picking up a red book in the library on a table, which leads to the sceptor which leads to the jewel box which leads to the usb dongle, etc... so time to go grab that book and do that chain.
You don't need the S.T.A.R.S. USB Key unless you want the L.Hawk/Magnum, which
really isn't needed (if you're speedrunning anyway, which since it's your first time through: Don't bother and just go for the Magnum).
The Club Key (green key) you got from that room is what you need to get the crank.
Spoiler: Club-key is exclusive to Leon A/B scenarios. Heart key is exclusive to Claire A/B scenarios, it's one of the changes they made in the scenarios (IIRC) where you don't need all 4 of the suit keys in each ones scenarios to get into areas. You get the crank for the bookcase in the same area, but getting to it with each character is different.
I'm honestly surprised you have been stuck on that since if you've explored the R.P.D. while Mr. X is chasing you, you've blown past a locked door that you should have the key for.
Reload your save, and head to the West Wing. You'll find the area, and then can get the second spare part you need to then haul ass back to do the puzzle with.
Also you can take Mr. X out for like 30seconds with two or so shotgun blasts to head (from a medium distance, anyway), but I really wouldn't bother wasting that ammo and if you've got spare Flashbangs, use one of them to stun him for like 15 seconds (in an open area to get around him) and haul ass between rooms and then be quiet as a mouse while you do your stuff, he shouldn't catch up unless you're blasting your guns around until you ring the bell in the clocktower, in which case you generally have a shortcut to get past him at that point.