You're right that the narrator is disagreeing with Sinatra. "Far from heavenly" is a strong way to say "not heavenly."
An important word in the sentence is the first word, though. Though is used to introduce contrast between two phrases; its meaning is like if but or however were used between the phrases.
The original text uses consequently, but this doesn't make much sense; that adverb should only be used when you're describing a consequence of something. For example, "All the shops were closed, and consequently we couldn't buy any food."
Otherwise doesn't need to be used here to suggest contrast, because though already does that. Furthermore, it doesn't make grammatical sense to use it here. Otherwise, as a conjunction, is used after a hypothetical scenario, such as an order or suggestion, to discuss the result if that scenario does not happen. But in this case, the first phrase is not hypothetical; it's not an order or a suggestion. It's a fact: Frank Sinatra did sing about the bridge's "lovely views from Heaven."