I do agree that ECC803S can have a forward, sort of aggressive, midrange (assuming you are talking about real, old stock, tubes); what is appropriate in one setting, or for a particular taste, is not appropriate in another.
I wish you the best in your search for a phono stage. It can be a daunting task given how many candidates are out there. I have not been in that market for a long time, so I have only run into different models incidentally. I heard systems that sounded quite good with Audio Note (uk), Lector (Italy), Zanden (Japan), and Doshi phono stages. I own a Viva (Italy) phono stage myself. If you like to fiddle around with your sound, you would love the Zanden because it gives you a choice of equalization curves. Sometimes, the "wrong" curve actually sounds better than the correct curve so it is nice to have that option.
Another option is to look for an outboard step up transformer to feed the MM input of your phono stage. While I know there are all sorts of theoretical reasons for eschewing step up transformers, I've always preferred the sound of systems employing them (my Viva has a built-in step up transformer). There are plenty to chose from, including custom-wound transformers made for your particular cartridge/application (look at myemia.com, a company noted for transformers and autoformers).