The solution might be: Either you play it safe and do without doorway pages or you use these and run the risk that one day your websites is completely removed from the search engines. The latter might be an option if there is not much to lose. However, if you have an established website or product, or if your company is well-known, we do not consider this as an option.
Instead you should concentrate on optimizing your websites so that documents having a real content are optimized for specific keywords. You should completely do without the sword of Damocles doorway pages.
Of course, it is not one of the easiest tasks to optimize a document for search engines and to include a reasonable content for the visitors on the other hand. However it is the safer method.
If you do so and you realize that you cannot integrate your keywords into the existing documents, create more documents that are more specialized.
While a doorway page is only created for attracting visitors to search engines, a well-designed website having an interesting content and being optimized for search engines can achieve more success.
For example, one of the advantages is that such a document has better chances to get links from other websites. This, however, improves the link popularity of your website, which is important for the recent algorithms of search engines.