A diplomatic victory with Venice is hard, and doubly so when someone is big and getting bigger by conquering all the city states. Most of the votes in the diplomatic victories I've won have come directly from city-state allies. Venice, however, can only really expand by consuming city states, so you're pinched in several different directions here.
I think you're on the right track by building up militarily, and trying to weaken the Ottomans via luxury starvation. If they've achieved a critical mass, though, it might not be enough to slow them down completely. It can at least give you a leg up in terms of production and military might if you can manage to push them into the negatives in terms of happiness.
I would not spend a lot of your resources devoted to this unless you can guarantee that outcome. Slowing down the rate of Golden Ages is not really that big of a deal by comparison to the crippling effects of severely negative happiness.
If you want to win, war seems inevitable. Luckily, the AI is pretty terrible at war. Unfortunately, war across oceans can often be difficult.
Given that you're in the era in which the Ottomans' special unit is coming into play, you might want to push hard on your science production to move past it so their advantage is lessened.
Once war begins, try to establish a well-fortified beachhead, and then turtle heavily. I would probably suggest building up quite a force and blitzing some major industrial area - ideally one that was originally owned by the Ottomans. That way, you can at least stage troops there, where there are hills and strategic resources. The loss of core cities hurts the most, but really you're going to want to choose a beachhead based on distance and terrtain more than ideal positioning.
Bring whatever long-range units you can muster, and station them behind defensive units for cover. The AI will tend to be unable to break this type of defense, and they'll send their units in like lemmings. You can use your naval units for support to weaken approaching troops or to harass their coastal cities.
Once their military resources are depleted, they will probably offer you territory in return for a 10-turn peace treaty. Take it, and then prep for another attack when the treaty runs out.
As far as the other civs are concerned, it sounds like the Ottomans are the major military threat - most of the other civs will sit on their hands or denounce you if you behave like this. However, let's face it - they're probably not going to like you regardless of your actions at this point. As you start to win, they're going to turn against you anyhow. The votes you need are going to come from liberating city states and allying with them.
Of course, once you've broken the Ottomans, taken vast amounts of their territory, and are the reigning military power on both continents, you're probably in a position to win whatever kind of victory you desire...