RMP doesn't put the songs in any order, your router is doing that via its DLNA server. RMP displays the lists exactly as the server provides them. As to skipping songs, I can't say, as I don't play music with mine. And I agree that almost any other option is going to require a stand-alone DLNA server. Most routers do a pretty lousy job of it, and other than your menu issue could be the cause of your other complaints. There are a number of DLNA servers that can be installed to a NAS device. Plex and Emby are two well supported on a Roku, and don't require using RMP. Serviio (and others) can also be installed on a NAS, but RMP would still be the player used.
Unfortunately, the Roku employee who was responsible for RMP just retired, so we don't know what sort of support will be available from now on.
Nvidia Shield, Roku Stick (3600), Ultra (4640), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.