My issue with Humphrey's disease is, given his drive to achieve the presidency even despite it - and after losing the election of 1968 and the 1972 nomination, and after the cancer had gotten seriously worse - I don't know if he would have resigned the presidency if it did pop up in his second term (should he win a second term). Even if Glenn were to be effectively the acting president because of it. Because I think its very dangerous to the effectiveness of the American government, I would hope Humphrey would resign from office if and when we was too sick and too injured by radiation therapy to effectively act as president. I'm just not sure he would if he was in office. Bear in mind, no president had resigned.
Bear in mind as well, this would not be a resignation of shame, like Nixon; a resignation over a matter that also hurt the party and aided the opposition to win more seats as a result. Humphrey's resignation, were it to come, would be one that was sad. It may be a less violent reminder of how Johnson attained the White House.
Depending on the year of this potential resignation, Glenn -like Ford- would be in a position to run for 1976. Depending on when Humphrey were to resign, Glenn -like Ford- would not be able to run in 1980 if he did win. Glenn -unlike Ford- would not have a shamed party, a jaded public, and the controversy of pardoning a criminal predecessor. If you google something like "John Glenn 1970", I would argue around those years that Glenn did look like a Democratic Gerald Ford.
If he did win 1976, he'd have till 1980, which would probably be a year the Republican party had a major chance of winning the presidency.
EDIT:
And my argument for that 20 year stretch of Democratic presidents is this: there are going to be years in that where the elections are competitive; years where the Republicans have a good chance of achieving the White House. The issue is, the can could keep being kicked down the road. The Republicans would have a good chance in winning 1968, but if they didn't, Humphrey (if not Kennedy) would have won and his incumbency, I would argue, would help him in 1972. Rather than it being perceived the Democratic party had been in office too long, I would argue it could be seen as Humphrey the person who is the Democratic candidate, rather than just the party, and Humphrey running for a second term rather than the Democratic party running for a fourth term. The Republicans should have a good chance of this alternate 1976, but the can gets kicked again in the scenario where Humphrey resigns and John Glenn becomes the president, because Glenn will have public sympathy, he's an American hero in his own right, and he will achieve incumbency ahead of the election. The American vice presidency at the time was not necessarily the conduit to the nomination, so had Humphrey made it to 1976, the nomination contest would have been a competitive field.
EDIT Deux:
However, it's important to note that is only one out of countless scenarios that could develop from John Glenn becoming a senator in 1964.