I would not waste time with using just any old cd player as a transport, a dedicated transport is the only way to go if you ever want to hear what your dac, and system as a whole, is capable of. Sure, an external dac can help a wee bit if added to a lesser or dated cd player, but if you can't afford to do both right, a one box setup will get you pretty close and possibly even more for your money if on a tight budget. The transports' impact is huge, at least as important as the dac itself. I would suggest selling your current player and either buying the best one box unit you can afford or split your funds pretty evenly and buy a dedicated transport and dac with good cables (don't forget the extra expense and clutter of addional cables!).
The Musical Fidelity A3 24 dac is one of the best I've ever heard, among many, and is very competetive with a couple of $10-30K digital setups I've recently played with, but ONLY when fed by a top notch transport. A couple of folks have posted less then enthusiastic results with this dac, but their transport where, to not hold anything back, crap. If crap goes in, only more crap can come out. In my experience, if you feed the MF dac through your cd player, changer or dvd player it can sound plain bad and you'll wonder what all the fuss is about, but give it a solid transport and it's simply magical, you'll leave any thoughts of going to SACD or vinyl far as possible from your mind. IMNSHO, for the price you'll find none better then the MF dac, period, very highly recommended.