As you lean back, gently try to bring your legs upwards. Be patient and do everything as if you are doing it in slow motion. You’ve got all the time in the world here unless you act like you don’t and move quickly; then your time on this earth might be ending sooner rather than later.
Once you are on your back, your buoyancy and persistence should allow you to get your legs and mid-section up floating on the surface. Now, ever so gently use your hands to very slowly paddle your way towards the edge using very short slow strokes. Again, everything should be done as if it is in slow-motion. Don’t submerse your hands all the way here. Also, try to keep part of your arms above the muck so you aren’t paddling with your entire arm. Paddling with your whole arm at too fast a speed will tend to make the sediment and water separate a bit around your body, which will decrease your buoyancy, which is bad. As long as you work in slow motion with small strokes, you should be fine either way, but good to be extra cautious.