Your analysis is excellent, MM! I believe that Michael was almost certain that Roth, not Frankie, was behind the Tahoe attack. But, as a careful man, he wanted to know for sure. Even more important, Michael wanted to know who the traitor in his family was.
Michael took a calculated risk in sending Frankie to meet with Roth. When he told Frankie that he wanted him to "settle these problems with the Rosato brothers," he said it was to make Roth think that "his deal with me is still good. Then he'll be relaxed, confident...and I'll be able to find out who the traitor in my family is." In other words, he was using Frankie to flush out Roth's intentions and (hopefully) to expose the traitor.
But, Michael had told Roth, "Frank Pentangeli is a dead man." As you said, Michael was too smart and careful not to know that, by sending Frankie to settle with the Rosatos, he'd be signaling Roth that he really didn't suspect Frankie in the Tahoe attack after all. And that Roth would figure that maybe Michael suspected him. I believe Roth ordered the Rosatos to kill Frankie so that he could eliminate a Michael-ally before Frankie and Michael had more chance to cook up some mischief against Roth. In doing so, Roth confirmed to Michael that he, not Frankie, was behind the Tahoe attack. Too bad about Frankie. Michael may have "liked" Frankie, but after Frankie mouthed off at Tahoe, he was just another obstacle to Michael's total domination of the rackets. He was expendible.
Michael's next step was to order Fredo to Havana to deliver the $2 million. Michael could have had anyone bring the money. He chose Fredo, IMO, because he he had some suspicion of Fredo and wanted to test him by bringing him close to Roth and Ola. And that's how it worked out.
This sequence shows how manipulative Michael was--another aspect of "Sicilian cunning." Another, underrated example of manipulation is how Vincent and Michael used each other in GFIII.