Suggestions to upgrade from Lyra Delos

I am a fan of Lyra cartridges.  I own a Titan, although these days a Transfiguration Orpheus L resides in my tonearm.  Lyra cartridges have a open, and nimble sound, which is not as harmonically rich and dense sounding as something like Koetsu cartridges.  If you want to hear something quite different, try something like the Koetsu Rosewood cartridge.  The downside to the Koetsu is that it will not sound as detailed, and nimble and it will not track quite as well as the Lyra,

A cartridge that I really like, because it sounds very vivid and immediate, without being harsh or thin sounding, is the Audio Technica ART 1000.  This is the one I would buy if I were in the market for a new cartridge.

Whenever I hear someone say they are looking for a cartridge that is more musical vs. detailed, I think that the person is looking for something that sounds harmonically rich or "dense" such as Koetsu or certain Ortofon and Grado cartridges.  The downside to these richer sounding cartridges is a sense of the cartridge being a bit muddy or "sluggish."  If you are not looking for an extreme contrast to your Lyra (which a Koetsu certainly would be), perhaps a Dynavector XX-2 might be of interest.

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).
  

It appears that you have done some trials on "free" or near free set up modifications, many of which can have quite a big impact on the sound.  I hope you have tried changing vertical tracking angle; for example, lowering the arm pivot point will add bass weight to the sound.  I found that the Lyra cartridges I have used are quite sensitive to changes in vertical tracking angle.  I hope you have tried changes in loading as well.  With most tube phono stages, less loading than utilized with solid state phono stages tends to work out well (less loading means HIGHER value of resistance, such as 47k ohm). 

Not so free changes that will really make a difference involve the tubes used in your phono stage.  Telefunken 12AX7 and 12AU7 run the gamut from warm and smooth sounding to lean and very punchy and dynamic; it depends on the specific tube.  I run a lean and dynamic variant (ECC803S) that has become crazy expensive.  You could try other tubes that are known to be on the warmer side (that warmer side is often the "magic" attribute some seek in tube gear).  To me, a pretty safe recommendation that almost always seems to please are Amperex Bugle Boy tubes.

Given that the Delos is quite a nice cartridge, Raul's recommendation that you at least consider a phono stage upgrade is a reasonable suggestion.  I don't know about your Hagerman phono stage, but, I do know that a good phono stage makes quite a difference.