I'd take this opportunity to move your website to a new host and a new content management system (the website editor system), your one looks pretty old and I sense that there's a number of factors here you're not happy with.
Assuming you control the domain you can point it at anything, so you'd just need to find a host/system that you like and is easy to use - here's some suggestions: Best Website Builder for 2022 - CNET - most of these will in turn handle all of the ssl/https stuff for you. Your website does have some custom forms, so that's probably the hardest part but you could consider just designing those in Google Forms and linking to them. You would then capture your existing site (screenshots, copy & paste content, download docs etc) and re-create it. You could for instance delegate archiving the content (PDFs etc) to someone else then take the job of rebuilding a new site yourself.
I understand that just fixing what's currently broken is a good short term strategy but it's not really sustainable. You could alternatively hire a freelancer to migrate it all to a system of your choice, then re-point the domain when it's ready.