I wouldn't touch Big Baby or Gooden. Neither is a starting center and if you sign either, that is all you have for years to come. You give up all cap space going forward.
I would trade Max/cap space for an expiring big (Boozer or other), sign Joe Smith for 1 year and make your play at Bosh/Amare next year.
Joe has to do a trade with this space. If he signs a backup big and makes no trades we're screwed for 3-4 years.