One point - does Congress meet earlier than OTL?
The Act of 1792 placed the Pres of the Senate and Speaker of the House next in line after the VP. However, in April 1865 there was no Speaker, as the new HoR had not yet met, and only a Pres Pro-tem because the Senate had chosen one at a special session in March. So if anything happens to Foster, he has no legal successor.
In this case, might Foster not feel obliged to summon, at least, the HoR so that a Speaker could be chosen, and even perhaps both houses to consider a new Act adding Cabinet officers to the line of succession?
One further thought, if he does the latter, and is also seeking some way to dish the Radicals, might Foster ask Congress to consider an Amendment repudiating the Confederate debt, and precluding compensation to former slaveholders - IOW, Sec 4 of the 14th Amendment, but sent to the States as a "stand-alone" Article. If this happened, it might be harder to pass OTL's 14A, which passed with only three votes to spare in the Senate, and fourteen in the House. Without Section 4, such an Amendment might have failed to make it.