Conditional Formatting Across multiple Cells Shortcut?

First, in my opinion, this design has a few problems. I will give you an answer for the sheet as you have presented it but the design is working against you. What other data is in each block besides the name and number? First, Excel works better when you deal with rows and columns. Creating blocks like this is not at all friendly to developing formulas to populate or analyze the data. Second, using merged cells creates many problems. So my primary advice is to completely redesign this.

Now, given the design as it is, here is the problem. You have a single conditional formatting rule for the "Jane Doe" block that uses an absolute reference to $C$6 (not C5, as your notes in the file repeatedly describe). As you have found you cannot apply that rule to the other blocks. The solution to this is to use relative addressing. Of course, this creates another problem, because that means that each cell in the block has to have its own rule to reference the correct relative position. You need four rules:

B2: =C6<=5
B4: =C6<=5
B6: =C6<=5
C6: =C6<=5

Note: This will also fill with red if C6 is blank. I don't know if you will really have blank cells there.

Once you have applied these rules to the first block, you can use the format painter to copy the entire block and paint the formats to all the other blocks at one time.

I have done this as an example for the red.

For Orange
=C6<=9

For green
=C6<=15

You must put these rules in the correct order for the appropriate one to be the one that takes effect (red first, then orange, then green). If you put them in the reverse order, then check "Stop" I think that will also work and may be more efficient.