Home page title vs. other page titles

Hi

I run the website for a company which is one of the highest ranking websites in its industry. The industry is relatively competitive and through years of effort the home page is rated between number 6 and 8 in Google for its most popular keyword.

Here's my issue - there are some lesser (but still very popular) keyphrases that are also contained in the title of the home page (which is the most important page of the website, with the most in-bound links). I rank between number 1 and 3 for each of these keywords, but it's the home page that is displayed in Google for these keywords, with an additional page link to the page that the keyword is primarily targeted to. The additional pages have titles and content directly related to their own keyword.

I'm thinking that if I remove the other keywords from the home page title, and just literally have the main keyword as the title without the extra text, it may increase my listings considerably for that keyword (there are currently 10 words in the title and my main keyphrase is just 2 words, but within the title the keyword features twice), but I'm worried that I'd lose placement for the other keywords for which I am ranked very high, even though the pages related directly to those keywords are very keyword friendly in the title, description and content of the page. The number one listing for this keyword has just the keyword in their title, but all of the other top-10 listings have additional wording.

I was also thinking of experimenting with this by changing it for say, a month, and then changing it back if I placement for my main keyword doesn't improve or I lose listings for the other keywords.

Can anybody help me with this? Do you think it's the home-page driving the high rankings for the lesser keywords or would I get the same placements if I removed those keywords from the home page? Another plus to this would be that the directly related pages would be the ones listed - which would be more relevant to the searcher. But I'm just worried that they'll drop dramatically.

And if I did experiment for a month by changing the home page title, if I changed it back in a month because it was unsuccessful, would I get my rankings for the other pages back or risk losing them??

And do you think my home page would increase for my main keyword if I made the title the keyword with no other text?

An internal relevant page will not only rank higher than the homepage(though it is a weaker page linkwise) but also will be more relevant and generate more conversion.