>> The file names that look suspiciously hopeful are called Virtual Disk-s001.vmdk and Virtual Disk-s002.vmdk both having approximately 4,151,424 KB. There was 1 other folder with extensions of .lck and 1 other file with the extension of .vmem that could possibly be the files we are looking for as well.

2 of them only ???
Do you also find a small text-vmdk with same name just without the "-s00*" ?
Do you have readable vmware.log files ?

>> The drive crashed and both an Apple and a nonapple tech could not get the machine to boot back up to recover my 20 years of Quicken data.
In my experience  most techs declare such a case as lost just to spare themselves the detective-work.
Most techs also assume that VMware makes the best vmdk-reading tools - unfortunately that assumption  is wrong.

Did you already try Photorec ?

Ulli