From your experience are any of the big cloud providers more effective/careful at this than others?

The big cloud providers use something like erasure coding across a collection of tapes (or hard drives) to preserve information. If you've ever downloaded something from usenet and restored it with quickpar, this is basically the same idea. Every physical cartridge gets a chunk of the file. Depending on parity settings you would have to lose many tapes distributed across an arbitrary # of locations to actually lose any data.

Note that the hardware the big cloud providers use for tape archives is very different from the devices the GP poster appears to have used, and usually have robust verification systems.

In addition the need for cloud providers to comply with userdata erasure means they have to frequently test their ability to read and write their backups - which should increase your confidence in their correctness. Yes problems can and do still happen, but IME far less often than the more traditional tape setups GP describes.

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