It would not surprise me to see things end without a true settlement as a result of a temporary cease fire holding because neither side finds a reason to resume shooting. However, that probably requires a ceasefire that restores trade to some degree, likely at least to the extent as things stood before the US and Israel attacked.
Ultimately, if the Iranian government can hold off the US without ceding anything, they can credibly claim that they won the conflict to their populace. The primary maybe not that comes to mind here is that the Iranian leadership has lost friends and family to the conflict (with the new Supreme Leader having lost both his father and wife), and that might make accepting a winning stalemate more difficult. That said, they are probably going to be more likely to put feelings aside to find a path forward than the Trump administration.
The hard part will be US sanctions against Iran. I don't think those get dropped for a ceasefire, but I suspect a work-around involving some combination of the EU, India, and China to be worked out. It's in everyone's interest (other than that of the US and Trump) to get Iran's oil back on the market and turn the corner on economic disruption, and the Trump administration can turn a blind eye and claim to the US public that they haven't given something up.
On the toll front, I think anything but Iran alone collecting a toll is potentially on the table. I see the main possibilities as (1) no toll, (2) a toll split between Iran and Arab countries that have been in the cross fire, (3) a toll split between Iran and the US, and (4) a mix of 2 and 3. The first two options feel most likely to me.
The next question is one of timing. My best guess is that the Trump administration will be reluctant to make a move they can't label as a larger win than the above (where "larger win" really means "smaller loss") until the midterm elections happen or the polls suggest that a blue wave a forgone conclusion. (I honestly can't imagine Trump being swayed by polling data--regardless of how dire--so this probably translates to when the midterms happen.) I would look for the midterms to give the Democrats the House, which would let them investigate the conflict thoroughly and block funding. As a result, I would expect the Trump administration to find enough motivation to find an end to the fighting sometime between the midterm election and the seating of the next Congress is seated in January.
That would be a lot of bad blood to put aside in very little time, but the conflict might be old enough at that point that the exit will be enticing enough to get something done. Iran might see an opportunity to extract a better position should Democrats make things painful for the Trump administration--especially if they cut funding.
That said, the potential of the Democrats actually forcing the end of the conflict is probably more potent than them actually doing so. If they were to actually do so, Trump and the Republicans would seek to pin the loss on the Democrats. From that perspective, a deal in the November-December time frame might actually be better than what can be gotten after a new Congress is seated, from the Iranian perspective.
