This is a complex situation and I feel like a lot more info is needed. However, there's a part where an answer can be provided, and it's whether to mix (or not) the times. And the answer is NO.
Check your own screen capture: you have 22h, then 14d and even 13m. And according to your description, these times are measuring different actions (one is for a match, the other for an initiated conversation, 2 totally different actions sharing the same data spot!)
What I'd do is to clearly separate the data for both actions while providing some visual information at first glimpse, then users could choose to learn more.
For this purpose, I'd add very clear text below the names, a visual "time lapse aid" over the avatars. Note: I suggest using monochrome versions for color blind users, but since you mention color aids, there you go. You could also consider opacity of the avatars, so 100% opacity is for 14 days and 0 opacity (just a hollow border) would be 0 days, so you can easily add CSS rules like the pseudo-code below
$opacity : $days_left
if $days_left=1 {echo '7%'}
elseif $days_left=2 {echo '14%'}
elseif $days_left=3 {echo '21%'}
....
Then, on a different visual and informational dimension, clocks only for hours and minutes and only as data for initiated conversation action. So, this clock would measure this action, and if action is not initiated, then clock is inactive and shows a "start" link to communicate affordance.
A quick mockup using your own screen capture:

remember: this is just an idea for you to get going, and more information is needed, but since you have it, I hope this helps you visualize the issues