Don't use strong tags inside an already bolded sentence. It looks spammy. It is something that you are obviously only doing for search engines and not for users. Google hates it when it finds that sites are trying technical tricks as opposed to doing something that also benefits users. If anything, I think this is more likely to lead to an over-optimization penalty for your website rather than helping SEO.
It isn't even clear that bolding helps SEO at all. See Does bold text really improve your search engine rankings? It could be a ranking factor and many SEO folks believe that it is, but I don't know of any studies that have shown an increase in ranking from adding bolding to a web page. I tend to think of bolding as one aspect of "prominence." Making text larger and moving text to the top of the page also make it more prominent. In my opinion, making text larger near the top of the page is much more likely to affect rankings compared to adding bold.
Now that Googlebot is rendering pages, using specific tags that effect the appearance of text isn't going to help. Googlebot will know that your entire phrase is bolded. It will apply all your CSS to the page. It will know that your <strong> keyword isn't any different than the text around it. Because of Googlebot's technical advances in the last few years, your trick isn't even likely to be effective for Google.
There isn't any evidence that keyword dilution (and by extension keyword density) have any effect on rankings. You have to use a keywords in a page so Google knows what the page is about. However using keywords multiple times quickly has diminishing returns in terms of SEO. It is clear that over-using keywords gets sites penalized. See Should I optimize the keyword density of a page OR of a site? In fact, many times Google prefers lower keyword density because that means there is more content.
Within a prominent phrase, there is some evidence that Google weights keywords near the beginning more than keywords near the end. This is because you are more likely to say the important things in a prominent sentence first. In fact you have done so in your example. I wouldn't worry about trying to draw the attention of search engines specifically to the keyword within a prominent sentence. They are usually good at figuring it out.
