I thought that once the House vote was taken, Ryan would become president and automatically lose his seat. If he didn't want the presidency, then he could resign, but he would still no longer be a member of the House. IIRC, the constitution doesn't spell out a process where they can decline. They just become the holder of that office.
I read the 1947 Presidential Succession Act as saying the Speaker would become president upon resignation of his office, implying that he could decline to resign and pass succession on to the next person. It does look to me, though, like once it gets down to the cabinet level, succession is automatic.
That law refers to succession after the President resigns or dies, so I don't think it applies to a case where Congress elects the house speaker to the presidency. Those who leave office at the end of their term don't formally resign, they lose power automatically.
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The relevant part of the Constitution here doesn't quite automatically make Ryan President, he could always refuse to agree to the oath of office. And I don't think it automatically resigns him from his current office either - when people in state office are elected to federal office, they have to formally resign their state office before taking office. When Obama was elected president, he had to formally resign from the Senate. So it seems like Ryan could just say no to the presidential oath of office, never resign the speakership, and remain as-is. Pence would become acting president for however long it took the house to decide between Clinton and Trump - although I'm not quite clear on one thing - with Ryan out of the picture as far as the EC goes, does the 4th place finisher come into play? - in real life, an EV was cast for Ron Paul. If that still happens here, maybe he becomes an option for the house after Ryan bows out.
Do we have any actual experts on constitutional law here?
