I like your basketball analogy! I was thinking, more of a very wide series of shells. If the spacecraft catches-up to the first wave, next the second, etc, until it is just ahead of them, then the ice took the hits, and they're cheaper material.

I also am *not* assuming some small intrepid voyager, traveling alone. Instead, I expect that all space industry will be focused around our star, until that point in time when the capital-into-capital *doubling* time drops. Once the *lag* of the journey to Proxima isn't enough to completely discount future earnings, you'll see a massive flux of capital equipment in that direction, *all at once.* After that initial rush, expected yields of new entrants will be low; we'll send a single, vast fleet to Proxima, then almost nothing.

And, considering all the materials needed upon arrival, then using the most damage-tolerant among them as a shield is reasonable. (Most large-scale vessels envisioned by futurists would use water tanks to absorb impact on the front of the ship... same concept, detached.) Your fleet, on arrival, unfurls reflectors, and uses that power to capture the laggard ice-walls, for local industry.

Similarly, reflectors here make the launch of all that ice a minor effort. A few grams of material necessary, per kilowatt solar reflector output, make it hard to worry about energy; elemental compositions are the limiting factor. Mercury'll have to go :)