I quilt my stuff (up to oversize king) on my Kenmore 385. I do the "puddling" method like so many others, and I still baste with safety pins for my larger quilts (starting to use glue for the little ones). I don't do a lot of fancy FMQ on big quilts, unless it is at the edges where it is easier to manouver.
I found it made a huge difference to wear grippy gloves - I use "Machingers", but lots of other options - and I found staying conscious of my posture important, too. I have a tendency to let my shoulders creep up by my ears which is exhausting AND makes it harder to slide your quilt around smoothly!
You can definitely do this, and I bet you'll be pleased by the results fairly quickly!
Alison