I cannot help but wonder what the purpose of this exercise might be. If you're looking to use Eikon for industrial data consumption, then Eikon is not designed for this purpose. Consider Refinitiv products from the Enterprise family, which are built to provide data on an industrial scale.
To workaround the limit of 2K rows returned by RSearch function you may request to order the results of the search by say market cap and request data in batches of 2K rows each using the result of the previous request as input for the next. E.g. order the results in descending order by market cap and in each request ask for all stocks with the market cap lower than the lowest market cap returned in the previous batch. You could do this in a loop using RSearch and DEX2 COM libraries.
Alternatively you may want to use more modern Eikon Data APIs and Screener instead of Search. Although Eikon Data APIs provide more modern interface, you'd still need to retrieve data in batches because it's still Eikon product, which is not designed for industrial data consumption.