I'm in the same sort of position. I project manage the roll out of SharePoint within my organisation, but I'm not an IT qualified person. I have a lot of SP experience of setting up workspaces and advising people on how to use it, and I've delivered a lot of user training.
Where I've seen jobs that require coding experience, I also ignore them, because I'm fairly sure that the jobs that ask for it, do need it. There are a lot of jobs that require working with the back end of SP, and those jobs will need skills completely different to the ones that I, and other people on this thread, hold.
Any implementation of SharePoint is a huge project, and requires people with many different experience and skills. I hope you'll find something eventually which matches yours more closely.
Soozi