... I would like to know what the maximum possible error that the D3 (functioning properly) can be. I don't want to rely on anecdotal recollections.
So this will depend on what you're defining "error" to be. If you want to know how far off a non-WAAS (since the D3 docs say nothing about WAAS) GPS can be vertically from the ACTUAL GPS altitude above whatever ellipsoid is being used as the surface reference, this:
seems to indicate that it could be <156 meters with 95% certainty. And that kind of matches up with the maximum errors I've seen on non-WAAS GPSs of about 200 - 400 ft.
However, if what you define the error to be the difference between the D3's displayed altitude and a barometric altitude, well, there's no way to know that, because the altimeter setting will have a large effect on what is displayed, and the WGS-84 ellipsoid and MSL are NOT the same thing. However, I don't think I've ever seen a difference between a non-WAAS GPS altitude and a barometric altitude of more than 500 ft., and with a WAAS GPS, no more than 200 ft. or so.
So if _I_ got stuck in IMC with only the non-WAAS GPS to keep me from hitting something, I'd add 500 ft. to whatever altitude I was supposed to be at (which already theoretically has margin built into it) and fly there (IOW, if I was assigned 8,000 ft., I'd climb to the D3's 8,500 ft.).
But if I actually only had one large EFIS screen and one ADAHRS to feed it and was going to fly IFR, I wouldn't use a D3 as the backup - I'd get a G5, GI-275 or an AV-30, so that I had a FULL EFIS with air data, albeit without a moving map.