The Saitek X52 and SST software has no provision for windows/offline calibration or scaling within the SST software itself. There is a window which shows that the controller and buttons are working correctly and the software lets you assign complex commands but there is no way to tailor the response, that must be done within AH's setup.
The nose bounce problem with the X52 seems to me to stem from two X52 issues. First, there is some mechanical play in the system at dead center which means coming off of center isn't always smooth. Also, the basic X52 has a plastic cone which will tend to stick once it begins to wear. The other problem is that the basic X52 has a very light spring and sometimes there is too little resistance to slight movements. While I like the light spring on the basic X52 I prefer the stiffer dual spring system and metal cone of the X52 Pro.
If you can't find a good combination of damping/scaling in AH that works for you stiffen up the spring. There are a few very easy fixes which may help you. Go to Saitek's forums and do a search and you'll find some suggestions. The easiest one I know of is to use the foam washer that comes with some bulk DVD/CD cases (the ones where all the DVD/CDs are stacked in a round case). Split the foam washer and stick it on top of the spring at the base of the control grip. If you can't find a case with this foam washer you can also cut out the hard plastic piece, it's about the right size but takes a bit of trimming. Another option is to do the same thing with a soda bottle cap (takes a bit more work). Also, it helps if you keep the cone lubricated with a little lithium-based grease to keep it from wearing and sticking.