Alternately, you could try this with a board implementing either the ATSAMD21 or ATSAMD51 chips--such as the Adafruit Itsybitsy boards. With these you could have either 10 bit output (at 44.1Khz sampling rate) with the 21 or 12 bit output with the 51. And, if you were so inclined, use I2S with an additional decoder board to get 16 bit! (IF you opt to go this route, make sure the chip has I2S capabilities--the 48 pin (smd) version of the 51 does not.)
Caveat: This approach will require considerable adaptation from the technoblogy code.
Incidentally, I had previously attempted to sort of "fuse" the short sample player code from technoblogy with the method described for obtaining 10 or 12 bit pwm output. Eventually, I just went with an ATSAMD21 board as it's got way more... well, way more everything as compared with the Attiny85, and I could store multiple (short) samples on a single board and have more than one outputting simultaneously. Also, while somewhat larger than the Attiny, these boards are (or can be, depending upon which board you go with and how many pins and such you intend to utilize) still quite small--which I needed for my particular application. *
* OK, maybe I didn't need such, but I'm a bit obsessed with fitting things into the most compact enclosure conceivable.