OP,
sorry about all the noise you originally received.
Yes, it is very likely you can significantly improve your sound with a better DAC. Typically, if you carefully choose you will get a very significant improvement when doubling your investment up to the average cost of your components. Just a general guideline I have found true. So, you could budget to about the cost of your preamp or amp. Fully investigate (not using ASR as a source of info) DACs into that budget. Be cautious if you want detailed oriented or musical oriented because in this price range it is easy to get highly detailed fatiguing equipment.