I found the best approach is to search LinkedIn for someone at the vendor that's closely connected to me, then compose a cheery message to that person introducing myself as a fellow developer and parent of a user, ask the best way to inject a bug report etc. This actually worked. Ymmv of course.
As someone this happened to, I was actually impressed they looked me up and reached out. Knowing they cared that much meant that I cared too and I was able to prioritise the request with the product team. When we completed the request, we celebrated, and even implemented uservoice on some sites to improve the feedback loop.
If I got a message like this I'd just block the sender. As a developer I have no say in what my owner tells me to work on. I type what they want and nothing more.