Somebody might be able to correct me on this but I believe that BackBlaze's vaults use vertically mounted drives, so that might be some useful data to apply to answer that question.
Don't know about relative reliability to horizontal mounts, but afair the drive manufacturer recommends mounting either vertical or horizontal and we didn't observe any obvious issues.
For what it's worth, a bunch of server OEMs sell top-loading storage servers, eg. https://www.servethehome.com/dell-emc-poweredge-xe7100-100-d...