well its funny how you couldnt 'feel' it before, then you answered that , the sidewalls where c=gone on the old tires,!!
may be a chassie issue that was being covered up by old worn tires, now that you have new tires, and the sidewall not giving way
maybe a relook at chassie, or bad shock maybe an issue to look at now ??
because it does sound as if a shock has went dead'
jmo