In your situation I would prefere to get a good quality dedicated CD transport. Having a good quality DAC means that you will hear all digital "dirt" that is comming out of the bad CD-transport/player. The integrated designs just seem not to have a jitter. Once you'll plug CD player into separate DAC you will find out the truth whether CD player has or hasn't the jitter. Also many people will say that they tried to connect different DACs onto their CD players and realized that CD player sounded better. That's often happen with low quality CD players that have poorly designed transport.
There are plenty of good used under 1k CD-transports that with your DAC will outperform today's $2500 integrated CD players! Check out Theta Data II, EAD T-1000...
There are plenty of good used under 1k CD-transports that with your DAC will outperform today's $2500 integrated CD players! Check out Theta Data II, EAD T-1000...