One candidate: Sciadopitys verticillata 'Weeper 2'. Source: Dennis Dodge. This plant is also probably called S. v. 'Weston Weeper 2'.

Here is a picture of another candidate: Sciadopitys verticillata 'R. W. Knight'. Or: S. v. ' Weston Weeper no 2'.

I'm still exploring the last reported weeper in the US. It seems to be difficult to obtain a picture. Material is secured by graftings. The mother plant is growing in deep shade and ought to be moved. The owner has problems doing this himself,

I was lucky to get a form from Bethlehem Nursery called 'Henge Form', IIRC, before Mr. Dodge departed this earth. Sadly, the plant was inadvertently neglected by me, and got overrun by weeds. It was almost strangled by a Celastrus, and I think they are trying again! But early this summer I cleared that area out, and I give it a better than 50% chance of recovery. It appears to be so weeping that it will need to be staked. But it is very slow growing, at least for me.

Someone else out there must have it.

I have 'Hingeform' that really is 'Haengeform' (Hängeform, German). The word means weeping, but a sound and vigorous plant will not be weeping. Maybe a dying plant will be weeping.

So you are saying you have seen mature examples of that cultivar and they are not weeping?

I have a 15 year old plant. Branches maybe horizontally growing, but not weeping.