November 1972 is months after space shuttle approval by Nixon (January 5, 1972). In the name of Cold War brickmanship the Soviet Union needs a space shuttle, too, even if they
hate the concept. Mishin is unwilling to scrap its N-1 and L3M lunar landing program, so he will probably be ousted as per OTL.
In 1960 Mister K. scrapped aviation design bureaus in favor of ICBMs. Since sence the respective rocket (MOM) and aircraft ministries (MAP) hate each others.
Bad luck: a shuttle is a cross between aircraft and rocket. Having both Soviet rocket and aircraft ministris working together is, by itself, a daunting task which explain why Buran started only in 1976.
https://books.google.fr/books?id=VRb1yAGVWNsC&pg=PA35&lpg=PA35&dq=Spiral+energiya+buran&source=bl&ots=UyY9kHkjHD&sig=ivdZlStUoRFrh19Pu414KqqQxZA&hl=fr&sa=X&ved=0ahUKEwim-eHRj9jPAhUDPRoKHTx3ADEQ6AEIPzAE#v=onepage&q=Spiral energiya buran&f=false
Now a shuttle launched by a N-1 would be quite bizarre - I wonder if someone could create a CGI of that thing ? With the N-1 first stage strange - pyramidal - shape it would be difficult to strap a big orbiter to the side. And if put on top there is all kind of aerodynamic issues.
One of the great projects lost with the N-1 was the 4N / 5NM big Mars rover and sample return. A 20 ton (unmanned) Mars ship.
The JPL has been fighting teeth and nails for four decades to get political support and funding for Mars Sample Return. It happened that 5NM had political support and funding but the wrong booster.