If I am you..
I take the rider w/double bagger and start there.
have 3 or 4 people start raking piles to dive into and bag hands and knees style.
as you are riding ..baggers on mowers will fill..ya jump off and pour those leaves into the bags not quite full from those hand bagging..
repeat..repeat..
without a rider and this thick the best approach truly is the rake..
if there are any decent kids in the neighborhood that aren't spoiled beyond approach I would hire them out at 10 an hour ..this biggest of yards even as thick as yours can be raked and bagged in less than 4 hours with decent help.
Sams Club..bags 220 in a box..
commerical can liners ..45-50 gal..
yellow box...25.00 including tax..
with more bagging riders it can be less time..
but with 3 decent kids ya can knock it right out..
my 3 youngest helpers can do 100 bags in 3 hours..including that I'm thirsty gotta pee break..
90.00 labor..25.00 bags..
problem solved..
that thick and probably damp I wouldn't try to mulch it out..
makes a big mess..
good luck..
just yell If I can suggest another way..