Fremont had already lost in 1856 and did not do much to redeem himself as a general when it came to fighting, even though he had done much to try to liberate slaves before being removed. It's not like he was winning battle after battle.
I think it is early enough that Foster is given several months 2 see how he does. Congress would be recalled, I agree, because then they would be able to run reconstruction right in their minds. And if a nominating convention doesn't come till mid August that gives 4 months to see how Foster does. They might decide to keep him in office for another four years.
The Democrats will know they don't have a chance, but whoever they nominate might get a few electoral votes. However the main thrust is going to be who the Republicans choose, and whether a small split comes. There might be one but I think it would be much more amicable than say 1912. And if everyone agrees that Foster is doing a good job there may not be a split. If there is, I suspect Foster might get some electrical votes even if he doesn't really want them because he is busy in the Senate. Several states may choose to still put him on the ballot as well as or instead of the really radical candidate, especially the states on the border like Kentucky and Missouri and Maryland.
Foster could also have a chance because the radicals could be more split than they want to be. The right be some still want Fremont. Maybe Sumner is a popular choice among some whereas others prefer Stanton even if he wasn't as popular as some.
However, the succession Act of 1792 was a law passed by Congress and not a constitutional amendment like the 25th would become. So, they could change the law. That might also factor in to the decision. Do they decide to change the law? And there again, Foster's performance in this crisis might convince them to do so.
Part of the question is also whether Foster would want to be president for an extended period. If Congress winds up being more powerful in the short-term oh, you might decide that it's better to stay in the Senate. However, I suspect that the Ppestige of being president would be too good to pass up. So, I think that he would remain if it were offered to him.