I'm sprung for a Shelter 901 for my LP12 - after using a Asak for about a week, and spending a little time with the Shelter 501. While my experience with analog and cartridges in general is limited, I have good ears and the Shelter 501 is famously good.
I believe the 501 is available at or near your price target.
I believe the 501 is available at or near your price target.