No one to become President! or- Who's on first?

From Wikipedia (take it with a grain of salt, but seems accurate)-

In 1881, after the death of President Garfield, and in 1885, after the death of Vice President Hendricks, there had been no President pro tempore in office, and as the new House of Representatives had yet to convene, no Speaker either,[11] leaving no one at all in the line of succession after the vice president. When Congress convened in December 1885, President Cleveland asked for a revision of the 1792 act, which was passed in 1886. Congress replaced the President pro tempore and Speaker with officers of the President's Cabinet with the Secretary of State first in line.

The Presidential Act of 1792, which would have been the law in effect during Cleveland's administration prior to the 1886 act, states that in case there was no president or vice president that the Senate pres pro tem is next then the Speaker of the House... nothing beyond that is mentioned. So... let's say Cleveland dies before the House passes the 1886 revision, my question is then in the vein of Laurel and Hardy- "Who's on first?"
 
For some information on why no Senate Pro Tem- George Edmunds ended in March 3, 1885 as Congressional session ended; December 7th John Sherman takes office as Senate Pro Tem with beginning of the new 49th Congress. It wasn't until 1890 that Senate Pro Tem's were in office until the next one took, there was until then always a gap between congressional sessions.

So our gap in this time would be somewhere between the assassination of the VP on November 25, 1885 and December 7th, 1885 when John Sherman takes office. And don't forget- whoever takes office is only ACTING President until an election can be held the in December 1886 according to the 1792 act; so even if Congress makes the entire country wait until December 7th, Sherman is not really the President and we'll have the first time an election is held that wasn't on the four year schedule; we'll still have a scheduled election in 1888 as well.
 
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