Well I veer this direction myself and hate the glare you sometimes get from digital recordings. Often its not the DAC that the problem but over-produced compressed recordings more suitable for car radios and low quality ipod/earbuds
First thing would be to get your T1 checked out to make sure its up to snuff as its possible some of the components may be past their sell by date by now. You can also experiment with some tube rolling if you want a slightly brighter or more euphonic sound. Personally I prefer the original Stax Gold Aero valves for the T1 but they are very difficult to obtain these days, so a good Japanese produced one (Toshiba, Matsu****a etc) are good alternatives as they are near to the original voicing of the amplifier. If you want to try something brighter then the RCA clear tops. Personally I wouldn't just replace the tubes for the sake of it as some service engineers fell obliged too. If they are still in spec and you like the sound then stick with them.
Personally I don't find the Stax bright unless the recording has hot treble and is that way inclined. The Stax have such extended treble in comparison to what else is out there some people interpret this as bright.
On the DAC front I would listen to some NOS DAC's first, like the Metrum and AudioNote. The battery based DAC's from John Kenny JKDAC32 and Ciúnas are well worth a listen.
Try comparing these to some of the over/up samplers like the Benchmak, Arcam, Renaissance etc whch might give you a hint as to which direction you want to go in. Often its not necessarily the DAC chip that has a specific sound but how its been implemented, output stage, jitter reduction, quality of USB implementation. So its usually the sum of the parts which make for a good or less good sound IMO.