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This is the second in a series of papers which consider the orbifolds ofpermutation-type as candidates for new physical string systems at highercentral charge. In the first paper, I worked out the extended actions of thetwisted sectors of these orbifolds -- which exhibit new permutation-twistedworld-sheet gravities and correspondingly extended diffeomorphism groups. Inthis paper I begin the study of these systems as operator string theories,limiting the discussion for simplicity to the strings with ${\hat c} = 52$matter (which are those governed by ${\mathbb Z}_2$-twisted permutationgravity). In particular, I present here a construction of the twistedreparametrization ghosts and {\em new twisted BRST systems} of all ${\hat c} =52$ strings. The twisted BRST systems also imply new {\em extended physicalstate conditions}, whose analysis for individual ${\hat c} = 52$ strings isdeferred to the next paper of the series.Comment: 21 pages, reference added and typos correcte

THE ORBIFOLDS OF PERMUTATION-TYPE AS PHYSICAL STRING SYSTEMS AT MULTIPLES OF c = 26 II: THE TWISTED BRST SYSTEMS OF ${\hat c} = 52$ MATTER