I think what you want is SymbolicLinks. You can use Symbolic Links to include a subtree of the wiki into a different place in the wiki.
For more information on SymbolicLinks, check your local users guide or the copy online: http://www.fitnesse.org/FitNesse.UserGuide.FitNesseWiki.SymbolicLinks
A common way to do this is to actually create your ParameterizedSuite and then symbolically link it into the Pages that define the configuration and supply specialized SetUp and TearDown pages. This is sort of the oposite of what you are describing, but I think what you are doing could work as well, provided you use SymbolicLinks to make the pages part of the wiki structure of your parameterized tests.
FrontPage
SuiteOne
TestOne
ConfigurationOne
SetUp
TearDown
SuiteOneSymolicLink
ConfigurationTwo
SetUp
TearDown
SuiteOneSymolicLink
In the structure above, SuiteOne can be run via the symbolic link in ConfigurationOne or ConfigurationTwo. Variables defined in the ConfigurationOne or ConfigurationTwo pages will inherit to SuiteOne when is is run via the SuiteOneSymbolicLink in each configuration hierarchy. Additionally, the SetUp and TearDown from the Confiugration Pages will be inherited as well.