I'd consider looking at PS Audio's new Perfect Wave DAC. The list price is a tad higher than your budget, at $2995 USD. However, they are offering a very generous trade-up allowance that is worth up to $1K off.
If you like the modded DL-III, then I think that this would be a logical upgrade option.
If you like the modded DL-III, then I think that this would be a logical upgrade option.