Here is the design idea I came up with for the new brand direction of OurTime. It is a bold and straight to the point icon, paired with a strong font. It will resonate well with your main demographic—they don't want frills, they want results.
The heart/clock icon can stand on its own, as needed, and I envision this really becoming what you are known for. Seniors and their families will see this strong icon and instantly think of you.
I know you asked for a blue/green color scheme, so I provided that: #37. I also included a couple of red/black schemes: #36, #38. I know this is an overused color combo in this industry, but it is for good reason: red and black evoke bold energy and positivity. If you feel it is a little too aggressive, then the blue/green you originally liked is a better choice.
I will see what else I can come up with, but feel free to comment on these in the meantime.
Here is a more clean, corporate direction: #39. I just wanted to give you other options, in case the more dynamic letters are not what you are looking for. This one is much more conservative.
This will look awesome on hats, tshirts, towels, etc... As I said, I see this icon as being the driving force behind your entire brand/identity, so it is important that you can see it looking great anywhere and everywhere you might need it.