"Exorcised" vs. "exercised" as a synonym for "agitated"

I saw this sentence in The New York Times and thought it was incorrect but now I'm not so sure:

"That's part of the political calculation that has party benefactors and leaders exercised."
_{The G.O.P. Tosses Steve King Overboard}

My thought was that "exorcised" would be correct in this context because I remembered similar use of the term from many years back. I always thought "exorcised" as an adjective or adverb had a secondary meaning of "overly agitated," as in "having a fit" but I can't find any reference that confirms my memory, nor do I find a definition of "exercised" that is synonymous with "agitated." I'm 68 years old and can't always count on my memory to be perfect any more, but this just looks wrong to me.

The connection between exercise and exorcise is that both, originally, seem to have meant to drive something from one place to another. However, in the OED, there is no real connection made between these two, so this may be a coincidence caused by the prefix "ex-":

exercise

Etymology: Middle English exercise , < Old French exercice = Provençal exercici , exercisi < Latin exercitium , < exercēre to keep at work, busy, employ, practise, train (compare exercise v.), < ex- (see ex- prefix1) + arcēre to shut up, restrain.

The etymological notion of exercēre is obscure: it is often regarded as having meant primarily ‘to drive forth (tillage beasts),’ and hence ‘to employ, set to work*

4.a. To give employment to; to engage the attention or feelings of; to tax the powers of.

1879 Cassell's Techn. Educator (new ed.) IV. 66/1 Various breeds had great celebrity—a celebrity which exercised the pens of their most famous writers.

exorcise:

Etymology: (? < French exorcise-r,) < late Latin exorcizāre, < Greek ἐξορκίζειν, < ἐξ out + ὅρκος oath.

1. transitive. To drive away (an evil spirit) by the invocation or use of some holy name; to call forth, expel. Const. from, out of.

1850 A. Jameson Legends Monastic Orders 23 Touched him on the shoulder with his staff and exorcised the demon.