19.5s do feel different than other tires. I can't say if you are feeling something strange or normal. I'm assuming they are tracking when there is a distinct indentation in the road. If so, that is just something to get used to.
80 is probably the pressure to have at max GVWR. The will get better with more wear. Some 19.5s are worse than others. NOTE: I've been running 19.5s for around 11 years with 4 different brands.
Oh, and the low profile tires on my Mustang track as well, so it's not just a 19.5 thing.