Passing cars on the right, and later merging into their lane
Seems to me that your best option is choice 2: Signal to the left in advance of running out of the lane, check for a reasonable gap in the cars while still moving, and merge into that gap once you've determined that it's safe.

In that option you are essentially behaving like exactly what you are - a slow moving vehicle.  Your behavior is like what you would expect if you were operating a tractor, or a horse-drawn carriage.  You operate in the lane when neccessary, move over to the right to allow others to pass when safe and convenient, and carefully merge back into the traffic lane when the shoulder is no longer safe.

While doing this you want to avoid weaving in and out of traffic every few feet.

This is also similar and predictable behavior much like what you need to do when the shoulder runs out as a right-turn only lane blocks your path.

Option 1 is unsatisfactory because you lose momentum and will have a difficult time merging.

Option 3 is a poor choice, not from the issue of passing cars on the right (which while legal in many areas, is dangerous), but because it's rude and then forces cars to pass you later - playing leapfrog.

Option 4 is a possibility, but then again, think about operating a 'slow moving vehicle.'  If you are consistently the same speed as motorists, you may stay in the lane, particularly if the shoulder is unsafe, otherwise, move over and let them pass.

Option 5 is the poorest choice.  You may be able to cross against the light safely, but not only is it risky, it makes you a poor ambassador of cycling, causing motorists to be angry at other cyclist, and frequently puts you back in the leapfrog situation.  Plus, you could get a ticket, at least in my town.