Ideally to get a perfectly accurate answer, you would review a comprehensive list of kanji, but of course that would be quite time-consuming. I suggest using statistics to speed up the process: Test yourself on a representative sample of the full set of kanji you want to estimate from, and extrapolate from that to get an estimate.
For example, what I have done in the past to get a similar estimate of the number of English, German or Japanese words I know is to start with a dictionary and randomly select a set of pages (more pages take longer, fewer pages make your estimate less accurate). Quiz yourself on every entry on those pages to get an average number of correct responses per page. Multiply that by the number of pages in the dictionary, and your result is a reasonable estimation of how many correct responses you should expect you'd get if you tested yourself on the whole dictionary.
You will need to be careful that your selection is actually reasonably representative. Depending on how the dictionary is organized this could be hard - for example if it's organized by grade level then entire pages are going to have a similar difficulty level.
There is a random kanji generator here: http://kanji.fm4dd.com/kanji-random.php that would be useful for doing exactly this sort of analysis. Unfortunately it seems to top out at the JLPT N1 list in terms of difficulty, so while it would be useful for less advanced users, it's not going to be useful for a reader at the skill level indicated in the question.