Google uses 2 main protocols, Imap and WebDav, the latter for contacts and calendars, mail and notes are Imap. Providers are not equal, are you sure that Lunarpages has enabled the hooks needed for notes.
I note your use of the word 'should' but I doubt that this is true:
though this is largely irrelevant, since IMAP fucntionality should not depend on one's hosting provider in order to work correctly
I stand by my statement;
If Apple's IMAP implementation within the new Notes app has been done correctly, it should properly interact with any server that correctly supports IMAP.
Here is the data I have:
- My Lunarpages IMAP mail works perfectly on my Android phone
- My Lunarpages IMAP mail and notes both work perfectly on my iPhone and iPad
- My Lunarpages IMAP mail works perfectly on my Macbook Pro
- My Lunarpages IMAP notes synced perfectly on my Macbook Pro under Snow Leopard and previous OS X versions.
- My Lunarpages IMAP notes DO NOT work on from the Notes app on my Macbook Pro in Mountain Lion (but again, DO sync correctly between my iPhone and iPad, and they DID work perfectly on Snow Leopard and previous version of OS X)
Based on the above isolation process, it is clear the problem is within Apple's implentation of IMAP within it's Notes app on Mountain Lion (i.e. this is a new bug not present in Snow Leopard), and there is no problem with Lunarpages IMAP, since I use it without issue on many other different clients besides Mountain Lion.
Additionally, if you reference an earlier thread in this post, you will find that we have determined the problem to be caused by the new Notes app in Mountain Lion not properly recognizing the IMAP Path Prefix server setting; the reason Gmail IMAP Notes work is that they do not use an IMAP Path Prefix. The reason my configuration does not work, apparently, is that I do in fact have an IMAP Path Prefix. This is consistent with others who are seeing this issue.
I hope this is enough evidence for you that this bug is with Apple's implementation of IMAP syncing within the new Notes app on Mountain Lion, and is not an issue with anyone's server service provider.