So with changes to various things, including giving our emails SPF and DKIM headers, it seems many mail providers have changed their policies.
Presumably, these changes are to prevent phishing, and this involves a large majority of support emails flagging as spam and not getting through to osTicket.
It seems a workaround in the current setup is not likely to work.
We should look into replacing Special:Contact (ext:ContactPage) with something to suit our needs. This may be that we use the osTicket API to file tickets via the RESTful API, using a similar looking form.
While we're redesigning this, it is worth considering if we can make the experience easier and help the user decide which medium they should be using - such as referring them to Phabricator, Hub Forums, Logo Creation Wiki, help pages, etc.