The way I read the literature, the Java Orekit version is the only publicly accessible version. If I am wrong, someone please tell me!
The C++ conversion was done later (2017-2020 vs. 2012-2015), by a group led by Professor Juan Félix San Juan of Universidad de la Rioja in Spain. They used to (2012) have a web site (http://tastrody.unirioja.es) where anyone could use standalone Fortran77 DSST remotely, but it doesn't seem to be there anymore. If you can find a copy of San Juan, López, Setty, and Cefola, "Validation of DSST C/C++ against original Fortran version: integration test", AIAA Scitech 2020 Forum, https://arc.aiaa.org/doi/10.2514/6.2020-0955, it has a number of interesting things to say, but it doesn't contain any code as such. More recent papers, like San Juan, López, Pérez, and Cefola, "Including the closed form $J_2^2$ effect in DSST", AAS 21-233, have stopped talking about C++ implementation, and moved on to adding new features. I'm not sure to what extent they are trying to keep the Fortran, C++, and Java versions synchronized with each other. To actually get your hands on the non-Java code, I would recommend contacting the authors directly.