It’s a good question, because the feature you are mentioning is very specific to the platform and not to models that have been embedded in a third-party application using the API. From the start, we had envisioned the platform mostly as a tool for designers and web developers to build their own applications, and not as the end goal of the users.
As it happens, it seems that more and more users are find with managing and sharing their models directly from the ShapeDiver platform, which encourages us to re-evaluate several features that were put on hold or even scraped. Sharing models with custom parameters is one of those features which will likely be implemented after all, even though it is a feature which can easily be reproduced by a third-party using the API. It will likely be done almost transparently by updating the model URL with each parameter change, such that if User 1 shares the URL of the model he is working on with User 2, the parameters will be encoded in the URL and seen by User 2 when opening the model.
As for a schedule, since we are currently re-evaluating several such features there is no deadline yet, but it is realistic to talk about a few weeks.