Spelling war erupts on the Red Line

that source contradicts itself. The frequencies you give are based on Google Ngrams, which give frequencies of words in Google Books by publication date. However it also quotes this passage from the OED:

"The word is found in spellings with -dgm- from the early 16th cent., and by the late 17th cent. judgment had become the prevailing spelling, although judgement was still commonly found. Kersey (1702) is an unusually early example of a dictionary in which the headword form was given as judgement . During the 19th cent. the form judgement gained in frequency in British contexts, and is now the usual spelling in general British use, but judgment has remained the standard spelling in British legal contexts when used to refer to a judicial decision (see sense 8), as well as in U.S. usage."

The OED isn't very consistent either, as its examples are dominated by the 'e' spelling until they get into the 19th century. The quotes from Milton and Pope are from 1667 and 1711.

No need, however, to restrict ourselves to just 2 choices. The OED also has this helpful table of variants, with the periods in which they were in use. ME is Middle English; numbers are centuries.

ME gogement, ME gugement, ME iugegement, ME iugemente, ME iuggemen, ME iuggement, ME iuggemente, ME iuggemet, ME iuggyment, ME iugment, ME iugumen, ME iugument, ME iuiement, ME ivggement, ME jewgement, ME jougement, ME jugemente, ME juggement, ME yugement, ME–15 iugement, ME–15 jugement, ME–15 jugment, ME (in a late copy)– judgment, 15 jugmente, 15–16 iudgement, 15–16 iudgemente, 15–16 iudgment, 15–16 iudgmente, 15–16 judgemente, 15–16 judgmente, 15– judgement, 16 judegment (perhaps transmission error), 16 jvdgement, 16–17 jvdgment, 18– jedgment (U.S. regional (chiefly southern and south Midland)), 19– jergment (U.S. regional (chiefly southern and south Midland)); Scottish pre-17 guegment, pre-17 iudgeament, pre-17 iudgement, pre-17 iugement, pre-17 iugiment, pre-17 iugment, pre-17 jugement, pre-17 juggment, pre-17 jugiment, pre-17 jugment, pre-17 jugyment, pre-17 jwgement, pre-17 17– judgement, pre-17 17– judgment, 18– jeedgment (north-eastern), 18– jidgment, 18– joodgment, 19– jeedgement (north-eastern), 19– jeudgment (Orkney), 19– jidgement, 19– juidgement; Irish English (northern) 19– jidgment.

Something for everyone!