I'm wondering if it's possible to define which modules Quartus synthesizes first. For example if you have a critical module that meets timing depending on the synthesis, could you tell Quartus to prioritize it so that it's fit optimally and other modules are fit around it?
You want to investigate the Quartus Design Explorer and the feature called Logiclock Regions. Basically it allows you to define a region (usually rectangular but does not have to be) and constraint particular logic to be placed into that region. This allows you to optimize the placement and routing on that module of logic.
If you want to close timing, I don't think synthesize your design in specific order will help. Instead, I recommend to checkout the application notes below:
Better than Logic Lock for this would be incremental compilation (in the Standard edition; called block-based compilation in Pro). Set the critical part of your design as a design partition. Compile your design and make sure that the design partition is meeting timing. If it is, you then "lock down" the critical partition so that it is not changed in future recompilations. You can then continue to work on the rest of the non-critical parts of the design.
You can do this along with Logic Lock, but LL restricts the placement options the Fitter has.
You don't mention if you are using standard or Pro, but here are trainings on this (with links to documentation):
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