polarised ... parboiled

parboiled ----- clipboard

clipboard ... parabolic (a good word for a math major!)

Waaah -- I didn't get to post leopards!

parabolic -- parochial

parochial ----- graphical

graphical ... altigraph

I have exhausted all my options and there are no words to continue with this word. Not sure if anyone else can find something that's a word!

altigraph -> altigraphs leads to some options for getting out of this corner

altigraphs ----- asphalting

asphalting ... scathingly

(From here, the best thing to do seems to be to drop a letter for a few rounds; one option for next round is "yatchings".)