I stand corrected. What would happen, though, after Ryan appoints a Vice President (or would he even do that since he is only acting as President? Would the new VP be an acting VP?)
Could an argument be made that now that there is a VP, he now becomes President as he is #2 in line and Ryan is #3, and Ryan was only acting as President?
A more significant problem is that it is a potential way for the Presidency to pass from one party to the other without an election. If one party held sufficient majorities in Congress, there would be motivation to remove an opposing President and VP in order to gain the Executive Branch as well. Conversely, the possibility that the Presidency might pass to the other party might dissuade members of his own party for voting for removal even in the face of overwhelming evidence of malfeasance.
The Speaker and President Pro Tem of the Senate were in the line of succession from 1792-1886, and from 1946 to the present. Between 1886-1946, the succession went directly to the Cabinet. It apparently was changed then at the behest of Truman, who believed that the presidency should pass whenever possible to elected officials rather than appointees. Of course, this principle was violated with the passage of the 25th Amendment which allowed for an appointed VP.
That would run completely against the separation of powers between the executive and legislative branches. You can’t be a member of both at the same time (with the exception being the VP double-functioning as president of the Senate - but that is explicitly laid down in the Constitution, and the practice of the Senate goes to great lengths to exclude the VP from actual business as much as possible). And I’m not convinced by the argument that when both President and VP are gone, that must be a time of crisis, so extraordinary things would be allowed. Your interpretation would actually extend this crisis period and delay a return to normal conditions until the next presidential election. Under the other argument, the Speaker becomes President, the House elects another Speaker (who is Speaker only), the President appoints another VP, and the country keeps going on as usual.