processing E-6 at home is perfectly feasible and many, myself included, do it normally.
I use a rotary processor, a Jobo CPP-2, which greatly simplifies things.
Strictly speaking though a rotary processor is not necessary and you will find people developing slides without it.
You will find plenty of threads in the forum about it. If you have any question, doubt etc. feel free to ask it in the Darkroom -> Color: Film, Paper and Chemistry section.