Steve,
It is an interesting and thought provoking attempt to clarify what does seem to be an intractable problem.
While it's not the topic of my entry in this essay, I would like to offer what I think is a minor adjustment to our concept of time that seems to have some consequence as to how we consider this situation. One which does lead to the 2nd solution, so you might find it of some interest.
I think the problem is that we experience time as a sequence of events and include it in our physical models as a unit of duration between events. I think we need to look at it from the other perspective, that change creates this sequence and it is not a progression from past to future, but change causing future to become past. To wit, the earth doesn't travel some fourth dimension from yesterday to tomorrow, but tomorrow becomes yesterday because the earth rotates. In this view, time is not a fundamental part of some foundational math, but simply an effect of action, similar to temperature. One could say that time is to temperature what frequency is to amplitude. Duration is not a vector that transcends the point of the present, but is the state of the present between the occurrence of events.
What this means physically is that there is no such thing as a point in time, since it would require freezing the very action causing it. It would be similar to a temperature of absolute zero. So one cannot actually separate a "particle" from its action. There is no "point" where it is just a particle.
Now what does this mean in terms of measurement? The same principle applies to the "observer"/measuring device. You are not so much detecting another particle, as you are creating an event. While the particles/actions/energy go from one event to the next, they exist as what we call the present. It is the events which come into being and then recede into the past. Ie, what was possible became actual. In QM terms, we are not moving along an external timeline from an actualized past into a probabilistic future, but are simply letting the events occur, such that the probabilities collapse into the actualities. What was future became past.
So while the laws governing the interactions are definitionally deterministic, the actual input into these events cannot be fully known prior to the event, as the lightcone is not complete prior to the event and even if information could travel faster than light, than so could input and the problem persists. So since effect necessarily requires cause, we can say those physical properties do exist, but there is no way to have definite knowledge of them prior to the event of measurement. Thus 2.
As for the ship, light has no internal activity, since all energy was been converted to velocity, thus nothing can go faster, as there is no more energy to propel it faster. So, no action, no time. Of course the external motion of this light does constitute a clock, the constant of lightspeed.
I do find the thought experiment a little silly though. If I'm sitting in front of the fire and I throw a log on it, does the clock of the wood go to zero, as it turns to light?