I am finding myself at this intersection quite frequently. From the N-S street heading south, I need to get across the street and I can trip the light OK, but my green/walk signal coincides with the green left turn for west bound traffic. Once I get to the other side, I have to wait about 60-90s until the green arrow is over which means I'll be at the end of 600ft line of cars. It will take 3 cycles for the light at the next block until I am at the next intersection 600 ft away at which point I need to turn right. The road is not wide enough for me to squeeze between the curb and line of cars.

I'm finding this is pretty annoying due to how long it takes to get down the street and there is no suitable alternative or out for the next 1/2 to 2/3 mi. Turning right at the intersection means I'll be mixed with 50 MPH traffic that cannot pass me for 1/2 to 2/3 mi at which point I'll have to turn left and go back the same distance to my destination.

so you are crossing the street with a green walk signal instead of the green light?

Looks like you're travelling from right to left in the pic correct?
And the traffic turning left is moving from bottom left to top left in your drawing correct?

Well, I'd go straight through the light on a gree signal only, that way there is no left turning traffic coming alongside you. I'd either stay with traffic if its the absolute best adn safe route, or filter up the far right side of the road. You say there is no space? Whats the shoulder? Grass? Gravel? Dirt? Guardrail? Cliff?

If you can filter up the side of stopped traffic its relatively safe IMO unless its a popular drop off (door-zone).
Ride like a car or a motorcycle, seems like traffic's slow and jammed in the area so should be relatively lower risk.

I need to go from bottom right to top left. The green and walk signal come on at the same time. South bound cars can only turn right here due to the design of the intersection. Traffic coming from the bottom left turning towards the top left gets green arrow at the same time as my green/walk signal since the design of the intersection doesn't really permit traffic to flow straight from bottom right to top left.

After crossing the intersection to the SW corner, I have to wait for left turning vehicles to clear before I can proceed otherwise trying to merge seems to be daunting task. I am hesitant to filter up because the right side of the street has angled front-in parking. I tried filtering once but I was constantly moving left and right to dodge mirrors and vehicles.

I've been taking the lane but taking 4-5 min to travel about 600 ft is pretty aggravating not to mention I'm kinda stuck in a stagnant plume of exhaust.

Sounds like a car accident waiting to happen. I dont see how you can have a green light to go through the interesection while the traffic to your left ALSO has a green light, albeit to turn left, which puts them on a collision course with your lane's flow of traffic. Complain direct to the city about this hazard, maybe someone programmed the lights wrong, cant imagine there are no accidents at this intersection with two lanes of traffic given green lights into each other.

But, if there is some sort of communication miisunderstanding and you are saying that "green/walk" is the pedestrian signal only and the traffic light is still red then:
Cyclists dont heed walk signals for pedestrians when in the lane of traffic as this confuses drivers and could cause a problem.

Wait for the green traffic signal, cross with your flow of traffic and then carefully either filter up, or take the lane and wait, annoying as it may be. Or take an alternate route. Or walk the sidewalk and avoid all the fuss while enjoying a few swigs from the water bottle etc.

Find a different route, or follow the laws. If that takes a long time, that takes a long time. If the light for cars is red, and the pedestrian light is green - WALK your bike across.

If you want the rights of being a vehicle, you get the responsibilities, too.

I think you're screwed. :-) It's interesting that south bound traffic needs to turn west/right. Is that perhaps because in the past south bound drivers wouldn't clear the intersection, and hence jam things up?

Are there any sidestreets you can bail out on earlier and bypass the mess, or are you limited to going through this intersection? (e.g. hang a right parallel with the west bound over to where you'd continue south)

South bound traffic cannot proceed straight through because there curb barrier that prevents cars from doing so. There is no car collision waiting to happen unless west bound vehicles run the light or someone tries to drive over the median.

Where I need to go is a block or two south. If I take the right, I'm on a 50 MPH narrow road, not wide enough for autos to pass me safely, for about 2500 ft before I can turn left and go back to my destination.

The thing that puzzles me is the bike arrow things that they placed on the road on the south side because there the direction I'm going is about the only safe way to get to it.

The green light and pedestrian light is green at the same time to go south, but autos can only turn right.

My problem is not getting across the street, but rather trying to merge in with traffic on the opposite side.

In every state in the US, bicycles are considered vehicles and are obligated to follow applicable vehicle laws. Assuming you're in the US, that should be the case where you are. Given that, you're not supposed to go straight, that's why there's a barrier/curb/whatever it is preventing cars from going straight.

The way I see it, you have four choices:
1- go right and if possible and the law allows it, make a u-turn and go right at the intersection to continue southbound
2- go right at the intersection and continue on until you can make a left turn
3- cross as a pedestrian in the crosswalk (some states allow you to ride across the crosswalk but still be a pedestrian, others require a dismount)
4- find another route