Thanks for explaining in detail Bob. Please do show the search hits in the relevant context or its exact position in the para with presetable characters (if possible) before and after the search hit in theexact location in its para, as google search does. I think FlexiSearch or any search script would do this. I will donate for this in addition to buying the plugin too.
I think Mathias since a text index does not take up so much space at all, even your 2000 posts would be no issue even for a full content search like this.
I know people export their docs and knowledgebases of tens of thousands of pages with such softwares like helpndo, etc. which create their own seamless and instant js search scripts built-in which generate such text indexes. And ajax wordpress plugins which do this by indexing 1000s of posts in a text index file. Of course I may be wrong in this but just sharing my observations.