If JEmplode is an option for you, you'll find it will do what you want (sort ignoring "The"). This is how I generally use it, with on-player sorting of menus disabled.

I also use the otherwise unused Artist field of my artist playlists and sort on those - that gets me "record shop ordering" where (title="Jeff Beck" artist="Beck, Jeff") sorts near to (title="The Beatles" artist="Beatles")[1]. You might be able to make this technique work for you in Emplode, too. Whilst entering artist tags on your playlists might seem a lot of work compared to hand-ordering your playlists, I find that copy+paste makes it less painful and that it saves time in the long run as more artists get added.

[1] The first two solo artists I thought of were Ozzy Osbourne and Sharon Shannon - neither of which illustrate this point very well!