Since I don't have Woodcock at hand, I'm not completely clear on the context. But sigmatic aorist is a term of ancient Greek grammar that has parallels in other I-E languages, e.g. Old Church Slavonic, Sanskrit, Old Irish.

Greek verbs in general have three stems: present, aorist and perfect. Each of these categories is aspectual--they describe the performance of the action apart from time. Present stem signifies a beginning and process for the action; aorist signifies the action, pure and simple; perfect stresses the completion of the action (and relevance of its consequences).

One way of producing the aorist is to add an -s- (sigma) to the strong or lengthened grade of the verb stem. So Greek λύω ('I am letting loose', present, with long upsilon) has sigmatic aorist ἔλυσα ('I let loose', also long upsilon); δεικνυμι 'I am showing' has sigmatic aorist ἔδειξα 'I showed'. Coming back to Latin, faxo is found in Early Latin as the future of facio (= Classical Latin faciam). Faxim would be the subjunctive from this stem--a subjunctive from the sigmatic aorist stem.

Preservation of these forms in Classical Latin makes examples such as Cicero's di faxint (Fam. xiv 3.3) and the examples from Woodcock easier to understand--they aren't 'perfect subjunctives', rather surviving present subjunctives from the aorist stem. Hope this helps!