I plan on removing the old device and using MasterBlaster to do this.
Is this the right means of attack?!!
Would the free version of altera Quartus II support this for me? I only need to program about 30 devices...
If indeed the part is the EPM7032QC44-12 then it is NOT jtag programmable, and you will need either a third party device programmer that can handle this part, or one of the old Altera Logic Programmer units with a device adapter card. Described here: https://www.intel.com/content/dam/www/programmable/us/en/pdfs/literature/ds/dspghd.pdf
You MIGHT be able to find a third party hardware house that has the capability to program these devices (7000 series, non -A/-AE/-B/-S parts) but this is really old school stuff now.
I personally have a EEtools (www.eetools.com) TopMaxII device programmer which has the capability of programming these series of parts (in this case with a custom TQFP44 to PLCC44 adapter) so if it is important enough to you to do this you might see about buying one of these. Software runs on a modern Windows 7/10 PC, does not require Intel/Altera software to read/program devices).
Good luck to you you are working on an old piece of hardware.