I wouldn’t be concerned about that. Businesses are strongly discouraged from badmouthing former employees unless you did something explicitly terrible or criminal. Worst case scenario is they would give no comment if given as a reference.
That’s the company’s problem, especially for a larger one. If a large company can’t handle having two people away at the same time, be it temporarily or permanently, that’s a problem with their staffing practices and not you or the other employee.
https://en.m.wikipedia.org/wiki/United_States_v._Swartz for a specific example. While he committed suicide before it was resolved it does show the kind of hammer that can be brought down from accessing public info
No issues requesting a missed pickup here. It can be quite common if they get overloaded, i.e. after a holiday weekend. It’s probably far more costly to do verification on every instance but they may look into it if it becomes a common pattern.
One thing you can do is apply a wash (basically diluted paint) over the laser etched sections, and wipe away the excess. This will allow you to color the etched sections that might look better then the printed version.