New drain field is okay. But that is not the problem
Toilet flushes okay, but with large poop it goes down slowly
After it breaks down the toilet flushes okay
Problem seems to be between the toilet and the outside.
Clean out plug shows water going out. This partial block
May be a tree root or something that hold up large items
Until they breakdown. Small items or loose material has no problem.
Guess need a camera to see what the blockage is??

I'm old school! 3 buckets of water is a good flush, AND cheap! That goes for every toilet in the house since likely they meet up somewhere as they leave the house. Never hurts to observe the flushing mechanisms when flushing solids, nor checking the functions of the holes under the rim, or the jet siphon function from that other hole at the bottom of the toilet.

I would start there before I got a camera guy out. You must first verify the efficiency of the toilet as not enough flush could be as simple as a clogged siphon jet as a tree root. Marked C below. (There are holes that get clogged with mineral deposits in B also, that should be checked and cleaned.)

http://www.plumbing-geek.com/images/xImage-05.jpg.pagespeed.ic.-6WbPi33hj.jpg

From: How Does A Toilet Work, Learn the basics of toilet function. DIY toilet repair. (http://www.plumbing-geek.com/howdoesatoiletwork.html)

When was the last time you checked inside the tank and its equipment? What type is it? Once that has been eliminated you move to the next logical step. Let me know what you find.

Note; You said the drain field is new. How new? What of the drain lines going to it? What are they?