I knew a win wasn't meant to be when my keeper goes down 2 minutes into the match and one of my better defenders draws a red card 2 minutes later.

4. Red card Crossfield (6) performs a hard tackle on Zamorano (2) and the referee holds up red!
3. Crist (8) passes to Filali (25) who is unable to control the ball and misses the goal by far.
3. Substitution Borrow (1) has to leave the field. He is replaced by McHenry (21).
2. Injury Borrow (1) appears to have hurt something.
Play starts when Crist (8) kicks off for Rocky Mountain Huskies

Ouch........I have had a run of injuries lately...

To fix your injuries, you should invest in your health center. With a high-level training complex you are much more likely to get injuries unless you combat that issue with an upgrade to your health center. Just yesterday my keeper went down and now he's all ready to play!

what health center level should one upgrade to so that players
can walk their injuries off
i.e. recover during the match
i.e. don't have to be subbed?

You cannot prevent injuries completely nor recover during match. From my experience, keep your health center at most 2 level below your training complex. More will be non-profitable, less will screw up your matches too often.

Level 3 will give you the option to use credit for healing injuries.

My health center is one area that I neglected greatly: L7 Training Complex and L2 Health center! :O I'm upgrading it now.......

I generally use the same rule for the health center. I might not upgrade it further in the future as I upgrade my training complex though, since the amount of additional injury preventation starts to decrease a lot after level 6 or so. The increase between level 5 and level 6 is more than half of the increase between level 6 and level 10.

It depends on the extent of the increase in injuries from upgrading the training complex though. The extent is not specified.