Finally got it: The way Eclipse picks up the JRE is using the system’s PATH.
I did not have
C:\home\SFTWR\jdk1.6.0_21\bin in the path at all before and I did have
C:\Program Files (x86)\Java\jre6\bin. I had both
JAVA_HOME set to
C:\home\SFTWR\jdk1.6.0_21 but neither of those two mattered. I guess Eclipse did (something to the effect of) where java (or which on UNIX/Linux) to see where Java is in the path and took the JRE to which that
java.exe belonged. In my case, despite all the configuration tweaks I had done (including
eclipse.ini -vm option as suggested above), it remained stuck to what was in the path.
I removed the old JRE bin from the path, put the new one in, and it works for all workspaces.