Rmihai, sounds like you are looking for the deal/bargain of the century. All those players you've listed are no where in the league of your player and budget. If you are looking for a player with those virtues, then I personally think you need to be a little more open minded and realistic to the DACs in general. I'm not sure why you consider them to be overpriced if you are looking for something in the 4-5K range especially compared to the Lin and Naim which is over 9K.
I've personally heard the Ayre and EC which are wonderful players (which are in lines to the players you've listed) and have compared them to the Bel Canto DAC2. Does the Bel Canto do everything better than those two, probably not, but comes very close (80%) for the money without breaking the bank. I've also compared the Bel Canot to the Arcam CD73T, Rotel 1072(?), and Classe .3 which are all within the budget you've specified. IMO, the Bel Canto came much closer in performance to the Ayre and EC than Arcam, Rotel and Classe.
If you were to follow your own general philisophy "of the system is to be as musical and pleasent as posible" and compared the Bel Canto or decent external DAC to what you are currently using, then I'd have to question how musical and pleasant is your system? Plus you've stated that " Hi-fi is a second priority", which to me the Bel Canto and DACs you've tried fit in that category. I'm interpretting what you meant by that statement is "budget system".
Yes, there are other budget players that can be modded to perform close to those you've listed, but then you're back to how much will it cost to have a player modded and stay within your budget? IMO, it's like buying a Civic and modding it to achieve the performance of a high end sports car (porche, vette), but it's still not the same.