Replace the lottery with a compensation auction until it reaches 90th percentile for the area and ban any companies with layoffs in the last three years. Anything else, like making it "skills based" will be gamed.
How about a French language teacher? https://h1bdata.info/index.php?em=&job=french&city=&year=202...
Pay more? Even on language learning sites there is variability on language and location. So if french language is that important so should the compensation be. You US will end up like Quebec https://www.ctvnews.ca/montreal/article/23-quebec-business-o...