As someone who also enjoys music in this vein, I'd recommend trying Ravel, Mompou, Janáček, Satie, Delius, Busoni, Milhaud, Fauré, Schubert, Liszt, Domeniconi, Sibelius, Ligeti, Messiaen, Xenakis, Martinů, and Scriabin among others I'm forgetting (in roughly decreasing order of likeness). Like you I don't get much out of most earlier classical music, with the major exception of Bach, or out of totally atonal stuff either.
20th century church music is worth exploring, too, whatever your faith or none. If you enjoy Fauré you should try Duruflé, and from there perhaps Howells.
The one I feel like I'm missing the most from is Mozart. To me Mozart sounds so trite, mannered, frilly, wimpy and boring. "Deeeeeee deedlee dee dee dee dee deeeee dee..."
FWIW, my favorite Beethoven pieces are the ones that sound the least classical in harmonic language -- especially the Waldstein Sonata and Sonatas 30-32.
Mozart can be hard to get. It's been said he was primarily a composer for voice no matter the instrument he composed for. His slow pieces are the most otherwordly.