I'm curious ... how do wise cyclists actually approach this issue?

Suppose you're commuting home, through a city. You have to cross water ( a shipping channel ), and there are only a few bridges. All of them have severe traffic issues during rush hour. You approach using the surface streets, and traffic backs up for all bridges. So, you're at a busy red light, and there are so many cars between you and the light, that it will take several light cycles before you get through. What do you do?

I'm of two minds about my options, but I face this question almost every day.

(1) I don't like the idea of dismounting, walking my bike to the opposite side of the intersection via the crosswalk, and then continuing my ride. It just seems absurd, nevermind that autos never do this.

(2) I really don't like filtering to the front of the line. It just feels unsafe, and I don't enjoy it. I do worry about "sending the wrong signal" to the cars, but wonder if I should? It's much safer for a bike to pass a car within a single lane when the car isn't moving, than for a car to do this at 30 mph when the bike is going 15 mph. But I bet that distinction is lost on the people watching the bikes go to the front of the line. Also, for what it's worth, I've been taking the whole lane more often, and filtering would seem to "confuse" the issue, as if I'm supposed to "pick" a single modality, and stick with it.

(3) It's ridiculous to wait for several light cycles. Traffic congestion is an auto-centric problem, and I have the capacity to avoid it. Nevermind the fumes I'm breathing from the idling cars; not being stuck in traffic is the #1 reason I stopped commuting in a car and started doing it by bike. One of the main advantages of bike travel is that the amount of time a trip will take is consistent, allowing you to make plans. This isn't true of cars exactly because of traffic, and it feels perverse and wrong to impose the same limit on bikes.

I haven't found my ideal solution, and I'm still exploring. But I've already learned a lot on this forum, and I'm hoping some of the answers people share might clue me in on something I'm missing, or give me some insight that would be helpful here. And if not, the worst that can happen is I'll have some other opinions to mull over...