Is the heat sink itself blocking the slot or the fan ? You can move the fan to the other side.
I mean it's not a big thing to remove the heat sinks, water coolers have been doing it to add water blocks sine the early days of WC. It is not as if on DDR2, the heat sinks serve any cooling purpose other than "looking cool". Mushkin makes it real easy, take a screw and ya done.
But if ya rush it and take short cuts (i.e. not using a heat gun), you could pull a chip right off the PCB. Still, if selling the old and buying new isn't an option, worth a shot. I would consider selling the old as using two different sets of RAM is not guaranteed to work together, even if from same company and same specs, especially so if their manufacturing...