At least half of them are derived from words that are almost not used at all in modern, everyday language. Those that are most... 'clear' would be:
April = Kwiecień - from "kwiat", meaning flower
July = Lipiec - from "lipa" known as the linden tree
August = Sierpień - from "sierp", the sickle used while working in the field
November = Listopad - the time when liście (leaves) (s)padają (fall).
The big count of Polish names of month came from Ukraine. I dont know about Polish meanings but can tell you about some of Ukrainian. I think it can help you.
March -березень - the month when береза(Birch) is awaking from winter sleep
May - травень - the month when трава(grass) is green fresh and young
June - червень -the month when червець ( cochineal bug) appear
September - вересень - the month when верес(heather) blooms
October - жовтень - the month when leaves are comming yellow(жовтими)
December - грудень - the month when грудки(pieces of hard cold earth) were in the earth
They should actually ranmdomize the sequence of the months and weeks because otherwise I can just use logic to determine which means which and get them right. I obviously would put extra effort but I don't know it feels kind of tempting when you hear the rewarding sound at the end of a trumpet. Please RNG the dates.