Particularly the first picture has some typical look of many interior bounces, the sort of substructure in the glass. (At least looks like typical things I've seen).
Nothing wrong with choosing a large number of bounces, it may be needed to avoid black sports.
There was a post about glass tables a few years ago where I calculated that around 200 bounces may be needed at extreme angles. viewtopic.php?p=25818#p25818
Most of the time such high numbers are not necessary though.
Only thing I notice is "Diffuse, Glossy & Specular : 32". That would sum up to 96 as the total maximum, so setting the total path depth higher shouldn't do anything.
(This also proves that your glass object does fine with 32 bounces as regular glass counts as specular)