I hope this helps a little.
We have an omega male who leaves a surprise in his food dish every so often. He does this because he can't get to the litterbox without someone picking on him and to sabotage the food so nobody else gets it after he's had his fill. It doesn't happen as often now, we know who does it and why, but it's still pretty gross. I have escorted him to the litter boxes many times and will continue to do this until the problem stops, if it ever does.
A former friend had female cat who did this as an act of rebellion when her owner was going through a busy time and couldn't give the attention she was used to getting. That cat ended up in an early grave because the owner felt she wasn't worth the effort and tossed her out of the house out of frustration.
I think the only cats that belong outside are bobcats and pumas, but everybody has a different opinion.
It doesn't seem to me that your kitty is lacking attention, based on what you've said, but there is something bothering the cat that would lead them to act in this manner. I'm not a specialist on feline behavior, we just have a lot of rescue cats and spend 24/7 with them, some cats are emotional and are more likely to display this type of behavior.
Your cat is lucky to have a caretaker who will not give up no matter how crappy (so to speak) the job.
They know they're not supposed to do that.
Other reasons may be medical but unless you noticed physical changes, unusual odors, bite marks, unusual anal discharge or wheezing, it may just be a phase.
Try mild voice commands and facial expressions (communication) that allow your cat to understand how you feel...and time. It may take a while but it's not impossible to correct.
We're not giving up on ours, I'll take poo over blood any day of the week.