Being that you have a Janome ... do you have the blue dot bobbin case? and are you using their FMQ foot (not the darning foot)? Both are add-ons that would not come with your machine, but are well worth the investment. I don't know if they will help with your invisible thread, but the blue dot is for tension issues, and the special foot is definitely a breeze for FMQ in comparison to the standard darning foot.
I'd also suggest you talk with your dealer and ask for their suggestions/solutions to your problems.
Ditto to the 100 wt Invisafil ... Or if you want a little more thickness then get their 80 wt DecoBob thread. Both are almost invisable and do a really nice job.