The Irish Code of Honour
It would appear that in the heat of the moment Mr Franz did not take time to review the terms of the Irish Code of Honour, or whatever variation of it was appropriate in the state of Illinois. To facilitate the opportunity to settle this dispute without recourse to further language unbefitting gentlemen of quality, I proffer a link (PDF) to an example of such rules, regrettably applying to South Carolina. I have not found rules for Illinois, but the rules proscribed for general adoption throughout Ireland are available for your perusal at the conclusion of the missive.
Duelling has been made illegal many countries to reduce the number of officers trained at tax-payers expense killed or maimed as a result of the rivalries among them. Although not trained in the law of Illinois, I beleive it may be possible to settle the dispute legally, within those parts of the code that do not reference firing pistols.
Spectators should note that throwing a glove to the floor is more than sufficient to enact a challenge to a duel. The challengee could pick up the glove and use it to slap the face of the challenger. In my humble opinion, such uncouth behaviour is beneath the dignity of a gentleman, and the code of honour inappropriate when one of the participants demonstrates the habbits and conduct of low born riffraff. The only honourable way to commence a duel is through failure of negotiations between seconds.
The code is intended as recourse for harsh words, or if a gentlemen were somehow taunted beyond all reason, exchange of blows. There is no direct reference to a dispute concerning settlement of a bill, but - at a stretch - such an eventuality might be considered equivalent to cheating at cards if agreed upon by seconds.
If Mr Franz has not already retired in shame at the depths to which he has sunk, and wishes to attempt to proceed as a gentleman of honour, he should request a friend (not blood relative) to act as his second. Such a friend would not be able to proceed in good faith without a written or public apology from Mr Franz including a statement that Mr Rutzokwski is a gentleman and the size of is penis is either unknown to Mr Franz or is of sufficient to escape the faintest hint of ridicule.
If seconds are not able to convince their primaries to settle their trivial pecuniary differences, the American variations of the code inevitably lead all concerned to criminal activity. The correct time to settle a matter of honour is at the first opportunity. The place is the traditional place nearest the primaries as agreed by the seconds. The weapons are smooth-bore flint-lock pistols. More modern pistols me be used if acceptable to both primaries. The seconds should also be armed as it is the duty of a second to shoot the opposing primary should he fire before the agreed signal.
Irish rules include a possibility for unconventional weapons. If the challengee proposes a sword and the challenger admits to being unproficient, the challengee can name any other weapon and the challenger must accept the choice.