Hiatus in presiential succession?

The Constitutions provides a temporary succession to the Presidency in the event that no president-elect and vice-president elect shall have been chosen and qualified.
From my vantage point, no hold-over President is allowed after noon of June 30.
But, judging the kind of decisions coming from the Supreme Court these days, you’ll never know.
There are loose talks from several quarters of a “failure of elections.”
The Commission on Elections has debunked such failed election scenarios.
But the Constitution is clear that when no President and vice president shall have been chosen or shall have qualified, or where both shall have died or become permanently disabled, the president of the Senate is next in line as acting president.
In case of the senate president’s inability, the house speaker acts as president.
In case of the inability of the senate president and the house speaker to act as president, the congress shall enact a law providing the manner which one is to act as president.
The problem is that the current senate president, Juan Ponce Enrile, is one whose term will expire also on June 30.
Enrile is running for re-election.
Nonetheless, by noon of June 30, Enrile will no longer be Senate President.
Enrile’s current term of office ends at noon on June 30.
With it ends his being Senate president.
There are suggestions that the Senate should already replace senator Enrile with a senate president whose term won’t end on June 30, but in 2013.
Unfortunately, the senate cannot just meet by itself, because it needs the lower house to convene also.
The constitution established a congress that is bicameral.
These days however, the house cannot muster a quorum because congressmen are busy for the elections.
There is one time where the constitution requires the congress to convene after the May elections.
The constitution requires congress to convene not later than thirty day after the May 10 elections to canvass the votes for president and vice president.
I see this as an opportunity for the senate to place in its agenda, the election of a new senate president whose term will not end on June 30.
If this will not happen, there can be a potential problem on temporary succession in case no president and vice president shall have been chosen and qualified, by June 30.
Let us assume there is no senate president because Enrile’s term also ends on June 30, and the senate hasn’t elected a new senate president.
The house also cannot elect a new speaker by July 1 because under the constitution, congress convenes only on the fourth Monday of July for its regular session.
Since congress convenes only on the fourth Monday of July (July 26), it cannot set up a manner of choosing an acting president.
Under such a scenario, who will be acting president from noon of June 30 to July 25?