I'm not sure 北方话 here means mandarin (官话) languages or the Chinese languages in northern China.
If the former, most 桂柳官话, i.e. southwestern mandarins in Guangxi, meet your requirements.
If the latter, some dialects in Shandong preserve the pronunciation somehow between palatal and velar.
A CCP political figure 孙政才, who is from 山东荣成, speaks with an accent ...