Sorry to be dense here, but what is "fundamental problem with the Constitution" which the DPP ha been diverting people's attention from? Is it China Issue 1 - that Taiwan is part of China? Or maybe China Issue 2 - that the ROC claims to still be the legitimate government of both mainland China and Taiwan? Separately and in combination, both are clearly weighty issues and not something that I think the DPP has a clear mandate to address (Tsai won, in part, by agreeing to maintain the "status quo" and following the ROC Constitution). Both DPP and KMT seem conscious of the issue and while I personally don't like the results, both have been pretty transparent in recent years about how they aren't going to change the Constitution to address either issue (at least not in the near term).
Also, while I wouldn't disagree that the DPP "manipulates" minds and espouse a Taiwanese consciousness, I am not sure how that is distinct from the KMT and others that manipulate towards a China consciousness. The DPP seems somewhat hypocritical to espouse Taiwaneseness while abiding by a Chinese constitution. And the KMT seems ridiculous by espousing Chinesness while hanging on to the hopeless claim that the ROC is somehow the legitimate government of China. That being said, both positions seem to be tacitly working towards what I perceive as the two baseline views of most Taiwanese - don't become part of the PRC and don't start a war with the PRC.