How can I find dependent rounding procedures with the desirable properties?
Dependent randomized rounding is a broad tool that is used in many approximation algorithms. Lot depends on the problem structure, objective and constraints and there is no single unified answer/framework. Some papers like the ones you mention identify generic settings where one has some nice probabilistic tools and provide some applications. I list a paper below that provides a more general framework and also has pointers to other work on dependent rounding. I also recommend looking at approximation algorithms books such as the ones by Williamson and Shmoys, and Vazirani to see the variety of dependent rounding schemes that are used.

https://arxiv.org/abs/1811.01597 by Nikhil Bansal unifying iterated and dependent rounding.