That corresponds to my memory. I'd go farther, that Carl wasn't even enthused about the business investment, but as the richest guy (by far) in the area he was persuaded that it was a civic undertaking to keep the team in town. The phrase "a cold Omaha" was current in that era, to describe the effect of losing one of the major sports teams.
Sid Hartman, I believe, coined the polite fiction that Eloise was some kind of driving force. You phrased it probably exactly right - she liked baseball, and Sid played it up on his radio show and/or in his column.
None of us are insiders, but I do think we have it about right.