Take everything I say here with a massive pinch of salt because I'm by no means an expert, and I'm just relaying what a friend of mine with much better knowledge of the USSR and China in particular told me when I asked in regards to my Under Twelve Stars timeline.
Essentially the big problem with comparing the Dengist reform of China with any equivalent alternate reform in the USSR is that circumstances are surprisingly completely different in spite of the shared red flags and yellow stars. As he put it, Dengism can be boiled down to doing essentially popular things that were only not done because of the ideological constrains of Maoism whereas any successful form of the USSR is going to instead be doing very unpopular things that weren't done because they were unpopular and the political system completely ossified.
The best way to do this (as in, keep the Soviet system functioning in some recognisable form) is to get Andropov to either die later or begin leading earlier, as Andropov has that understanding of the neccessity of some kind of reform while also being sceptical enough of liberalisation to prevent the kind of Glasnost or Perestroika that would undermine communism. He also has the understanding, unlike many late Soviet leaders, that communism was not inevitable or invincible. His experiences in Hungary in 1956, where he saw secret police lynched in the streets during his deployment, dispelled that illusion for him. In this way he is the closest you get to a Soviet Deng; but again, the comparison stops there because of the differing circumstances.
For Deng, the solution to China's woes was to basically implement most of the policies that developing countries tend to implement to set off an economic boom; the economic liberalisation was largely removing restrictions on what people could do as much as it was accomodating business leaders. For Andropov, "saving" the Soviet Union is much worse for the average Soviet person. You get a tough period of austerity to get public finances in check, including the cutting of wages and other social benefits. The only real plus for "ordinary" Soviet people is that there might be some accomodation of small scale private enterprise; other than that, ruthless political Stalinism and public sector austerity.
In terms of how this relates to the public perception of the USSR; I don't think this kind of path is going to do it many favours, but who knows. Andropov is I think a pretty ghoulish individual like most late Soviet leaders, but it's not impossible to imagine that he might cultivate an image of a pragmatist outside the Union. Overall, though, I think you'd still have that pop culture perception of the USSR as a big bad, especially as the political Stalinism is likely to continue (and the influence of the KGB likely to keep rising).