Yeah that first link makes a lot of sense, this issue is common since the model needs to be prepared to do QAT but the prepare step happens at some random point within the PL framework (not at start) so loading into it before the prepare is what causes the error.
This is primarily a PL issue, but you should be able to circumvent it by creating a new PL module that does the quantization prepare stuff right after model load rather than at the checkpoint hook. You could for example call it manually before loading (though there may be issues with preparing a model twice if the quant prepare step in PL doesn’t check for that).