Okay, you are doing too much work. I haven't checked so I'm not positive, but I suspect if you converted your lossless files to mp3s and set the destination to a location on the disk drive that is not watched by Auto Import, you could save some of that work in deleting the mp3s from the library.
But regardless, what you need to do is read,
very carefully, this Wiki article:
https://wiki.jriver.com/index.php/Sync_Handheld You need to understand and get the settings right.
Please search the forum for "Sync Handheld" and/or "Handheld Sync" as there are some detailed discussions about how the functionality actually works. Glynor has written a lot about it, and is a heavy user of iDevices.
Then I would be doing something like this.
Once off preparation:
a. Create a directory on my hard disk which has sufficient space for all mp3s I may want to transfer. Make sure it is not in a location where MC Auto Import is watching.
b. Set iTunes to watch the above directory and import any mp3s that appear there into its database, but not move the files. Just index them. Set iTunes to automatically forget any mp3s that disappear from that directory.
First synchronisation to my iDevice:
1. Create a playlist in JRiver for the albums I wish to transfer to my iDevice. Add all the albums I want to that playlist.
2. Set the Handheld Sync functionality to convert everything to mp3s. Use the Handheld Sync functionality to sync the playlist to the location created above.
3. Check iTunes has my music. Sync iTunes to my iDevice.
Done. Finished. I wouldn't do anything else.
In future, when I wanted to change the music I had on my iDevice:
i. Edit my synchronisation Playlist by adding and removing albums from it, as required.
ii. Use the Handheld Sync functionality to sync the playlist to the location created above.
iii. Check iTunes has my music. Sync iTunes to my iDevice.
Done. Finished. I wouldn't do anything else.
Improvements to the process:
Then I would play around with using more than one Playlist so that I could divide up the sync a bit. Maybe have one playlist per Genre. But also maybe set up real Playlists, because they are synchronised to the hard drive location, and potentially to iTunes, along with the mp3 files. I understand you don't really want to ue Playlists, but heh, it never hurts to try stuff.
Notes:
Mp3s are small, so I wouldn't bother deleting the converted versions of my files between syncs.
When you use the MC export feature to add files to iTunes on the computer, incorporating file conversion, MC uses a cache of the files anyway. So a copy is left behind on your computer until you clear the cache. I don't recall details of where the cache is located, or if you have to manually delete the cache contents. I think you can turn the cache off, but that may be a global MC setting from conversions. Anyway, all that means that using the Sync Handheld functionality doesn't really use much more space. You just know where it is, and how big it is, rather than having the files in a cache somewhere.
I wouldn't try to put all my music on my iDevice. If I did want to do that, then yes, I would probably delete the mp3s from my PC after the sync.
The MC Handheld Sync functionality will convert new files added to my Playlist and sync them to the hard drive location. It would also delete the mp3s that I have removed from the Playlist.
Whenever I say "Playlist" above, I would really be using Smartlists.
Caveat:
It has been a while since I played with Sync Handheld in detail. I may have gotten something wrong.