Or was he, like Harry Truman seems to have been, of the opinion that Chiang Kai-shek was beyond saving? Or did he just not give the issue much thought?
Truman didn't give up on the Nationalist cause from the very beginning - he actually did try to extend a considerable amount of aid to the Nationalist cause at first. In 1947 when the Nationalists made an urgent request for a 4-year aid program, Truman recommended that the USA grant $570 million in aid for fifteen months. However, Congress slashed this amount to $400 million and it wasn't implemented until the second half of 1948, by which point the Nationalist cause was pretty much hopeless.
But going back to your question, the Nationalists did try to directly cultivate relations with the Republicans, having become disillusioned with the weak support they were receiving from the Democrats under Truman, and believing along with most other people that Dewey and the Republicans would be ousting Truman in the 1948 election. Dewey declared in June of 1948 that he would extend massive military and financial aid to China if elected. Of course, he never got the chance to do this and so we won't get to know exactly what form this "massive aid" would've taken. Truman ended up rejecting two additional pleas for help from the Nationalists in November and December of 1948. By then, most people in the USA felt they should be getting out of the conflict as soon as possible, and they even felt a Communist China was tolerable (if not desirable) compared to the alternative of a massive intervention from the USA.
Source: The Rise of Modern China, by Immanuel Hsu