Change a Niche/Offer – Change my website?

After watching Doubling My Business and doing the Narrowing Your Niche worksheet, I have **picked** 1 offer and a niche, which is different from what I originally set out (and different from what I’m truly passionate about).
My previous niche/offer was “I help 30-something professionals actually achieve the goals you set with my tested formula.” This is my true passion, but it’s much harder to monetize on.
My current niche/offer is: I help third year law students at Tier 3 and 4 law schools get a job. I have done this before for clients, I know this is monetizable, and I know exactly where those thirsty people are.

My question is: should I change my website copy to speak specifically to the niche / offer? Currently, my website is much more broad (life coaching). Or should I just make 1 landing page speaking towards the law student offer?