There's a bunch of great stuff out there that's good to explore. Helena Sheehan's "Marxism and the Philosophy of Science - A Critical History", basically goes through the historical development with respect to the Philosophy of Science within the Marxist tradition. Typically in the US, we basically get treated to our own history in relation to the problems and paradigmatic shifts that went on within the philosophy of science. Typically it starts with Mach, the Vienna Circle, Carnap, and then moves onto Popper and Kuhn, which turns to Lakatos and Feyerabend, etc. However, its not as if Marxism doesn't have its own intellectual tradition, with its own problems in relation to the philosophy of science, and so starting from Marx and Engels, she basically takes you through the history of ideas within the Marxist philosophy of science, and how they figure within the larger socioeconomic context in which they were brought about in. It's basically a materialist conception of the history of the philosophy of science within Marxist tradition starting with M&E up to the Comitern period.

If you want to learn about some Marxist attempts to solve the measurement problem, maybe check out David Bohm's pilot-wave theory, which was largely overlooked then (1951) due to his then Marxist views and refusal to rat out fellow communists to HUAC. He later gave up his Marxist views in 56 after the Hungary Uprising, and ended up basically becoming more of a Hegelian, and I believe he dropped the theory. Despite that its still one of the more well known alternatives to the Copenhagen interpretation, with the Many-Worlds solution probably being the more popular in media.

I should also note that he was also overlooked due to the almost cult-like following Niels Bohr held within the scientific community. However, this wasn't limited to non-Marxists. His right-hand man, Leon Rosenfeld, professed Marxism to the degree that Pauli once ironically addressed him as the squareroot of Trotsky x Bohr. Yet, he was a staunch advocate of Bohr's complementarity to the degree that he basically tried at every turn to shut down Bohm's attempts to popularize his pilot-wave theory. In 51, Bohm received a little support from Soviet physicists in opposing the Copenhagen interpretation, but for the most part they preferred their own solutions compared to that of Bohm. Here I refer to Dmitrii Ivanovich Blokhintsev, who from what I've been able to find out on my own, may have formed something akin to a precursor to decoherence. The book I'm reading which goes over the history of the Copenhagen interpretation doesn't cover any of the Soviet physicists in depth, so my general knowledge of Soviet physicists is pretty thin.

Lately, I've seen Carlo Rovelli talking about Lenin and Bogdanov's epistemological debate which basically ended up splitting the two apart irreconcilably. Basically, Bogdanov believed that Marxism needed an epistemology which could readily contend with the new problems posed by the advances made at the turn of the century within physics. Needless to say, but Lenin thought otherwise. If your interested in Bogdanov, check out the Bogdanov Library as they just posted some links to a mini-symposium they just recently uploaded which includes a lot a pretty neat lectures, one is aptly titled "Conversation on Philosophy of Science / Scientific Philosophy Facilitated by Mike C. Jackson: McKenzie Wark and Carlo Rovelli – Bogdanov, Lenin, and Scientific Philosophy." Also another lecture compares Bogdanov's project, Tektology, and it's relation to Stafford Beer's own beliefs and development of Cybersyn in Chile under Allende.