I have to agree that Dewey wouldn't accept the second slot on the ticket, and I believe that he couldn't anyhow: if memory serves, technically Ike's residence at the time of his nomination was New York (recall that he was president of Columbia University at the time). That would mean both the presidential and vice-presidential nominees would have been from the same state, which is constitutionally verboten.
Assuming the speech is unconvincing and assuming that Dewey does not give "keep Nixon" advice, who should supplant Nixon? This warrants further consideration, but I don't think it would be Lodge: that would be another easterner from the more moderate wing of the GOP, which wouldn't play well in the midwest. My sense is that it would be necessary to get another westerner with something in the way of ties to the more conservative wing. I question whether Everett Dirksen would have accepted the second slot (but the fact that he was from Illinois sure wouldn't hurt), but it's a thought--and he had clear ties to the Taft forces in the party. Perhaps either William Knowland or Earl Warren might have been acceptable overall?
As a sidebar, what becomes of Richard Nixon if he gets dumped from the ticket? He'd probably finish out his term in the Senate (to which he was elected in 1950), and given the relatively low level of the accusations against him, might be able to get another term in 1956. Then what? Possibly a run for governor of California as in OTL in 1962, which he might be able to win after two not-unsuccessful Senate terms. After that...a possible run for the presidency in '68 from the governor's chair in Sacramento?