My main question is: is there a problem with putting pid files in non-standard locations?
Not in principle. Pid files have their problems (something may throw away the file, the pid may have been reused, race conditions if you don't use locking (but if you use locking, why have a pid file?)), but they are just a file. Of course, if there's some program checking for pid files, it may need to be told where the pid file is, but other than that, not really. Perhaps you may have a higher risk deleting the pid file if the file is in your home dir, but that's more a procedural issue.