While you wait for a reply, I have some ideas for you to think about.
1. I don't know what you mean by the PDF SDK, so I will assume you mean the Adobe PDF Library. This isn't available for download but the documentation for it is part of the Acrobat SDK. Look at the plug-in reference. Now, many plug-in methods are not available in the Adobe PDF Library, especially all of those starting AV, but you can see what is available. In any case it is licensed for use via DataLogics, and while the original library is C/C++ only, they provide various additional functions and platforms.
2. I don't know the abilities of LiveCycle products, but they do have their own forums and experts.
3. Looking at the actual requirement. First "compress" is not a term ever used for PDF in this connection, because it's confusing. PDF files are already internally compressed. What you want to do is reduce file size I imagine. Now, this is not magic - you cannot have a program which will "always make files smaller". But there are certain very specific things that can be done. For example, image resoluion can be reduced. Of course, this will have no effect if there are no images, or hey are already at a low resolution; and it is easy to reduce quality below acceptable measures. Please be very specific about what you want to do, and we can tell you what is realistically possible. I strongly suggest you try out the PDF Optimizer for a wide mix of your files, try it out, see what reduces, and have stringent quality tests.