I appreciate that you used sources from some very reputable authors.
I'm not totally convinced that aspartame is having deleterious effects on mental health yet.
Aspartame is likely degraded in the gut and all of the breakdown products can be obtained from foods. However, a single high dose of aspartame could plausibly disrupt the gut brain axis and cause problems
The study you cited did use a high dose of aspartame (2g for an 80 kg person!) For reference, a can of diet coke contains about 180 mg.
The difference is depression score was clearly higher in the aspartame group but I would have liked to see a positive control in that measurement (ie: how would that difference compare to a depression score in a person clinically diagnosed with depression).
Also good points on arachidonic acid but I think the other benefits of eggs (choline, lutein, cholesterol, omega-3 fatty acids in pasture-raised) heavily outweight that risk when it comes to brain health.