I don't like mixing with the cars so anything that is not that. I'd probably wait to reach the end of MUP and take whichever green light is on. Either the left or the front crosswalk. And then wait on the opposite side for the other green light.

Legality for your area aside, what I'd do is on a green bike across the cross walk then position myself in the north east corner, in the bike lane on the east side of the intersection if it's safe, at the pedestrian waiting area if not, then bike across the roadway into the westbound bikelane when east-west traffic may proceed.

No matter what, always remember to look behind you to your left to make sure no one is trying to overtake and turn right when you are about to cross an intersection.

I don't know the actual best practice, but my 2 Canadian cents:

For complex intersections I personally cross on foot both ways. I'm not a particularly experienced street cyclist so whenever I come to an intersection that's not well designed for cyclists I tend to take the safest option.

Depending on the speed limits and personal abilities I think we should be able to take the intersection as a street vehicle but in my neck of the woods people don't know what the heck to do with a cyclist and can make some poor decisions.

Better to be slow than flattened by a lifted pickup that didn't even see you lol

Another option, depending on how busy the road is. Go straight across on green, bang a u-turn when it's safe, then turn right. Or hang a right at the light, u-turn, and go straight across.

Neither should be necessary, but there's an intersection I sometimes go through with a similar setup (albeit without bike lanes, just wide shoulders). If traffic is clear coming north, I get in the left turn lane and wait there, but if not, I'll go right and turn around. The other problem at my intersection is that the left turn is triggered and a bike won't do it, so that's another consideration.

That cross section layout reminds me of a Tom Scott video: https://m.youtube.com/watch?v=SYeeTvitvFU

2 cyclists dead in 10 years before, but now the one dangerous cross section has reportedly been turned into 2 safer "t-sections" (if that's a thing).

A full explanation as to why accidents happen there, from before the changed cross-section layout, but on a shitty website unfortunately: https://singletrackworld.com/2018/01/collision-course-why-this-type-of-road-junction-will-keep-killing-cyclists/

Edit: unlike the cross section of the op, the Isley cross-section had less traffic and no stoplights, so there was nothing that forced traffic to come to a full stop before crossing, which made the oblique angles that much more dangerous.

I normally do C, or A if it feels too dangerous to join traffic.

What's the speed of the road? I would personally join the road earlier so that I can manoeuvre across with the traffic, but if the road is super fast I'd probably pick A. That is unless right on red is permitted, then I'm not sure.

I usually go with c. There is one particular intersection where pressing the pedestrian cross button causes an all cars red all crossings walk (only 3 though) phase that I abuse to do b, but it's not actually allowed. It's just a really dangerous street and that's the only way to not get killed by clueless drivers that don't know hand signals.

I would cross the EW street on the MUP 90% of the way and put myself at the front of the pack on the east side of the cross street and wait for a green. Personally preference, not saying it's the correct way to do it.

If the cars are driving fast I'd just use the crosswalks but if it's something like 25 mph then I'd just use the lane to turn left.

I would go with C, taking complete control of the right lane (ride about 2/3 to the left of the lane), using hand signals to make it clear where I'm going. If it's not safe, I'll fall back to A.

B is always unsafe and illegal in my area. A and C are both legal in my area, so I'll pick whatever is safer at the time depending on traffic. I've done both in my area, which has roads posted at 35mph and 45mph (so 60-70kph), and people often go 50-60mph (80-100kph). It's scary the first few times, but I can usually time it for either a red light or a lull in traffic.

A is always going to be safe if you wait for the light to change, it's just time consuming. So I usually try to make C work.

Cross to top-right corner, wait for light to turn green in the left-facing direction. That is the safest, and also correct, way of doing it.

The "FHWA Separated Bike Lane Planning and Design Guide" includes a version of this layout and the intended directions for bicycles

It seems the intended action is to not turn left/west at all, you're probably expected to cross to the NE corner then sit in the lane waiting for that green light. Unlike accessing the shared-use path from every other direction where a left-turn isn't prohibited by design.

If you want to take this to your local council to add those refuges you can bring the FHWA-SA-18-077 and make a pretty solid case. It's pretty damn simple to paint a green box in the westbound lane so that everyone is on the same page about how bikes can safely go west. Check if your local DOT has an ArcGIS or similar website that tracks things like bike Average Daily Traffic and ped/bike accident reports for that area.