As an LEO in Illinois, I want to touch on a few things.
First, like Arkansas, it's a crime to resist arrest in Illinois, even if the arrest itself is illegal. 720 ILCS 5/7-7. Unlike Arkansas, Illinois makes no reference to the fact of the officer working under the color of his responsibilities/duties. Depending upon how one resists, it can be charged as a misdemeanor 720 ILCS 5/31-1 Resisting/obstructing a Peace Officer, no officer was struck or hurt, or as a felony, the arrested struck, 720 ILCS 5/12-4(b)(6) aggravated battery, an officer, or caused injury to him, felony under 720 ILCS 5/31-1 (a-7). And that's not including if the officer dies.
Second, like previously mentioned, one needs to know their use of force statutes, in their state. In Illinois, those are 720 ILCS 5/7-1 for person, 5/7-2 for dwelling and 5/7-3 for other property. Note, 5/7-4, which defines the aggressor, and defines when one can be the aggressor in a use of force situation.
In short, you would have to be very clear in your actions against an LEO. You would have to be able to articulate very clearly why you acted in the manner you did.
I'm going to amend this part, see the conversation below with better details.
Lastly, I agree that the easiest solution would be to comply and deal with the situation later, in a civil court as well as a criminal one. Of course, this is mute if the situation is a clear cut life or death call. That said, I'll emphasize the clear cut part. Again, you had better be able to clearly articulate why you did what you did in resisting, and or combating the LEO.
Are there bad LEOs? Yep. Do we make mistakes? Yep, we are human after all. Yet, the badge does not put us above the law, but does hold us to a higher standard of it, IMHO. That said, the badge can cloud other's view of us, and to what standard of the law we should be held too. Think about that as you consider your response to the OP. In some areas, it will make you a bad guy regardless of what the reason, and in others, it will mean you are a hero.
If you ever find yourself in this situation, I hope none of us do, I would hope that we would all do the right thing, regardless of consequences. As I learned early on, "pray for the best, prepare for the worst." If you do react to a situation as presented by the OP, that is a quote I think you'll live by for awhile.