Most of this you probably know but I just want to post for other readers.
The problem is because you are requiring loans outside of the Fannie/Freddie conforming markets. Conforming guidelines only allow for up to 10 properties. Outside of the conforming market you'll have to look for financing with Alt-A (portfolio) lenders. As of 8/3/07 that sector of the mortgage market took a huge blow and we're still feeling daily effects of lenders chaning guidelines or closing their doors.
I have a list of about 7 lenders, all who still allow for unlimited properties. None of them have an Alt-A program that allows for Cash Out with No Seasoning.
However, I do have 1 lender that can do cash out with no seasoning up to 75% and allows up to 10 properites. Their guidelines do note that over 10 properties can be approved as an exception. An exception usually requires a strong file...job history and assets.
One thing to keep in mind also...stated programs are starting to change as well. Many lenders are limiting stated programs to self employed borrowers only, no w2 borrowers.
There's one other lender out there that will do this at 70% cash out but the rates are in the mid 11s with a couple points.
You could also refinance your existing properties held for 12 months with a bank that does commercial loans. I know one that does them at 75% which would clear up properties held in your name giving you a fresh start of getting up to 10 again.
Rate/term is a whole other story...no problems there with seasoning, plenty of options.