The latter question, on convening a new congress with all officers unavailable, is very untested. Especially in the near-doomsday scenario where the government is essentially wiped out at the same time (including the "designated survivor" etc.). The issue of how and on what authorities each new Congress is convened in a formal legal sense is largely untested in the courts, because such issues rarely come up, and even harder would be for someone to have standing.
But it's not completely untested. The best court precedent would be Powell v. McCormack (1969). This concerned an elected representative, Powell, being denied his seat while the House performed investigations on him. Ostensibly this was done under the constitutional provision that the House (and Senate) would have the power to determine the qualifications of its members, and with a 2/3 vote to expel them. In particular, they were determining his qualifications. The holding of SCOTUS was that this was unconstitutional: that the only action Congress could take subsequent to such a determination was expulsion, a power which attached only after the member(s) had been sworn in and seated, so excluding him was a constitutionally invalid action.
All of that doesn't sound terribly relevant until you get into the nitty gritty of the court's logic. To quote the wikipedia page's summary (emphasis mine):
The Court found that Congress is the whole body of initially candidate members who have been elected by the laws of the several states (in and for each state's apportioned congressional districts), who assemble at the seat of the federal government on the 3rd day of January after the preceding November's congressional elections. On that date, they are sworn in by their individual oaths of office and thereby collectively become the Nth Congress (89th, 95th, 105th, ...).
...
The challenge to the Court in its analysis and decision was devising a proper course of action that was both coordinate and consonant between the sovereign authorities (the Congress over itself and its members, the people and the states over the Congress) each in their own sphere, over the choosing of members to the Congress. The Court looked at the historical precedent of the House, the history of its candidate members, and the role of the states and their voters in choosing their representatives. The Court concluded that the US Constitution (the word and will of the people), the weight of history (the record of how the people have used their constitution), and the federal structure of the government (the role of the states in organizing and managing elections within their borders) required the Court to decide that the sovereign will of the people, as expressed in the democratic process, and the coordinate role of their states must be made consonant and held supreme, in the responsibility to create candidate members for the Congress.
The people, by their Constitution, affirmatively posited, defined, and delimited all qualifications for standing in elections for membership in the Congress. The states, under the 9th and 10th amendments explicitly retain unto themselves the power to make the laws for the government and regulation of elections for federal offices that are apportioned to them (the states) by the US Constitution. Therefore, the people and the states together have the sole authority for the creation, production, and generation of candidate members of the US Congress through the operation of the laws of the several states and the articles and clauses of the US Constitution. Thus, the Congress itself is become a creation of and subordinate to this process. Congress's processes and procedures for the management, administration, and discipline of members (once they have taken the oath, been sworn, and entered upon the rolls) are constitutionally subordinate to the sovereignty of the people and the states respectively over the creation of the membership of Congress.
The take away from this is that the formal procedures you document for inducting a new Congress are not mandatory for the creation of that new congress. It is via the authority of the states themselves that each Congress is created. All that needs to be done is for the candidate members to take the oath, be sworn in, and entered upon the rolls. The first two require nothing particularly special. Any judge or notary public can administer oaths and have them sworn in—Lyndon Johnson was sworn in as President by a notary public: his own father—, and even in a doomsday scenario there should be one of those somewhere. The "entered upon the rolls" is maybe the only peculiar one, though I imagine a court would accept any entry by anyone as valid as long as the Congressional chamber in question does not itself question their validity.
Thus, the Congressional rules you found simply make the process predictable and uniform: of all the possible ways to be sworn in and entered upon the rolls, this is the particular ways and particular peoples to be normally used. As courts have also held that one Congress cannot bind the next, it also strikes me as unlikely that the courts would force a new Congress to abide by the rules of the previous Congress as regards their induction. Especially since doing so in such a hypothetical nightmare scenario would impinge upon the authority and power of the states to create each new Congress.
This is, however, my opinion.
