The crit thresholds are very close (for A crits, 71 for skin vs 75 for plate; for E crits 111 for skin vs 109 for plate). But this applies after the armor DB mods, which as you noted are -15 for AT 1 and -50 for AT 20. So that's a -35 offset. (The weapon mod sometimes shifts things in the same direction, sometimes not, depending on how well suited the weapon is for penetrating armor.)
Step that offset back and you'll see the actual IAV needed to achieve an E critical is 126 for falchion vs skin and 155 for falchion vs plate. For A criticals, it's 86 for skin and 121 for plate. (This also includes the weapon mod.)
Now compare the table in Arms Law. Falchion vs AT 1, A critical at 85, E critical at 124. Falchion vs AT 20, A critical at 121, E critical at 147. The CCS yields results that are fairly similar to Arms Law.
There happen to also be a number of issues with the tables in Arms Law, many of which are being addressed in RMU, but assuming your intent in using the CCS is to try to replicate the Arms Law tables, it works pretty well.