How does the Yamaha DX7 digital analog converter work?
Indeed all 16 channels are time multiplexed and stored into sample/hold stage for later summation. The sample/hold stage is controlled by the SH pins from the OPS. I have no exact details how it works, but there are two sample/hold stages so most likely half of the channels are summed together into one S/H stage, for reason I don't know. Maybe they are alternated by odd/even channel, or 8+8 channels, due to analog performance, leakage, etc. It can be solved by taking a look at SH pins with scope (I don't have a DX7, please figure out if you do).
The DAC itself is 12-bit, but external to the DAC is an analog multiplexer which can divide down or shift the analog value so the result has a 12-bit precision but larger range. Sort of like floating point values, with 12-bit mantissa and 3-bit exponent to halve the value 0 to 3 times. The analog shift stage is controlled by SF pins from the OPS.
The DAC reference input comes from a 8-level R2R DAC, whose digital value is loaded by DACCE pin from the MCU. It is set by the volume entry slider. So it's a 8-level volume control. When compared to TX7, it has 64-level but it has a fixed DAC reference and the volume level is set with a VCA later in the analog path.
Basically, they had no reasonable cost DAC available with reasonable performance, so to get the wanted analog performance, they had to put more common 12-bit DAC there and do analog shifting and summation of channels.