The OP did a lot of work learning French, it’s always interesting to get a peek into someone’s process for something impressive and out of the ordinary. So thanks for the long and detailed write up.
I wanted to point out that the limitations that were encountered are normal. The OP learned 95% of what can be learned without living in the culture itself. Sure, you could learn all these extra details by chatting online, but it’s not until you need the vocabulary to get something from the French bureaucracy or to do your job that it all sinks in.
1. Don’t worry about Québécois, most French cannot understand it either. I once saw an interview on French public television that subtitled the French (Québécois) in French. To the French from France, it’s a very heavy and rustic accent, such as an Irish or Scottish brogue to an American English speaker. And it has its own local variations, such as between urban and countryside, with all its own idioms as well. The subtitled conversation was an old person in the country, young urban dwellers know to speak slower and clearer on purpose, unless they get familiar with slang and cussing.
2. Verlan is also just slang, interjections, and cussing, what the young and hip youth speak to be unintelligible on purpose. It also has overtones of poor, working-class, and immigrant identity, thus many layers and uses. Many words have made it into mainstream speech, though never into formal or newscaster speech. And when verlan words became mainstream, the original speakers just flipped the words again and kept on going (not sure if there have been 3 reversals yet). Like in any language, familiar speech can be a minefield: what’s used and appropriate depends on whether you are speaking to friends, homies, co-workers, managers, shop-keepers, bureaucrats, family, children, etc,
3. Phrasing just takes time and exposure to native speakers. All languages have these subtleties, such as gynmase salle de sport and how they are used, so you can only learn them through exposure, not vocabulary decks. Plus the concepts are cultural as well, sometimes we don’t have the equivalent concept in American culture, and vice-versa, the concept you want to convey isn’t apparent in French culture (for example, membership gyms with weight rooms and such are relatively new in France). The salle de sport might be closest to a rec center or the Y, but both have slightly different cultural connotations in American English as well. This sample also shows how you are/were translating phrases and ideas from English. They sound vaguely off to a French speaker because they would approach the whole topic with different concepts and constructs. That level of expression cannot come until you live in the culture for years and interiorize it’s thought patterns.
4. Verb tenses have rules and everything, but they later just boil down to an extensive vocabulary: you just memorize the words for each case, in the sense that your brain just knows the words for each subject-verb combination. We do the same in English for a few remaining times we use complex tenses: would you have known, what could you have done, etc.
5. All languages blend and trim words, dontcha know? The French do have a tendency to speak quickly, and compress some of the extra wordiness of the language—so it happens even more than in English.
6. For complex or technical topics, again it’s just about learning extensive vocabulary and word combinations. French isn’t that difficult a language to learn (compared to others) but both English and French have some of the largest vocabularies meaning there is a huge mapping from one to the other. French also has centuries of cultural expression and academic publication, and has thus developed both a special style and vocabulary for many domains.