Might not be the answer but new tires can be squirmy. As the mold release compound wears off & the go through some heat cool cycles they tend to firm up & should be like the ones you have. Most people notice it changing from run flats because of the sidewall stiffness of the RFT, but am surprised its that noticeable going from the same tire to your new one.
Was the tread pretty much done on the old tires? Higher new tire tread can also make them feel funny
2014 435M-Sport - 2013 135is Cab JB4/ISO 6MT - 2009 V-Star - 2009 Ford Expedition EL 4X4 - 2003 Xterra 4X4 - 1998 Ranger 4X4 - FFR Cobra MK-IV
work in progress