Installing GFCI into a box that feeds two other outlets
You are correct the number of wires for box fill is limited by code. I would be feeding the GFCI on the line side and pigtail the load with #12 wire. You are kind of stuck with what you have it’s going to be a tight fit hopefully it is a deep box. I have replaced boxes that were two small with old work boxes and in some cases used a 4 square box with a single device mud ring, this provides the most room but requires a bit of Sheetrock work to close it back up. Each box has the cubic inches allowed stamped on it. To calculate how much you need it’s 2.25 for #12 wire, we only count 1 ground the 3 hot,  the 3 neutrals is 7 a 2x for the the receptacle 9  plus if the box has clamps another for a grand total of 10 x 2.25  so the box would need to be 22.5 cu inches to meet code. Hope that helps I believe this is the reason they say no more because standard boxes are not that large and a GFCI device is larger than most receptacles but the same full calculation is used.