Buy new CDP or just add a newer DAC?

You've received good arguments for going with a DAC and I would add a couple more.

The area of audio where a lot of the innovative development is happening now seems to be in DACs, quality is going up and prices are dropping relative to the quality. A separate DAC makes for an easier decision if you want to upgrade.

Conversely, the part of a CD or DVD player that's ultimately going to fail is the transport and it's often not possible to get a replacement mechanism. Having it uncoupled from the DAC means not having to give up a perfectly good DAC when you need a new transport.

There are lots of good DACs in your price range. I, too, would recommend the Simaudio Moon 100D. I liked mine so much I upgraded to the 300D.