Is it possible to make DH_Counter count up to a specific time and then hold that value?

Yes, let's imagine that you want the counter to start at 0.00 and count up to 4.61:

1. Put DH_Counter clip in the timeline at the default duration of 10 seconds
2. Set Type to "Stopwatch" and check "include zero"
3. Scrub through the timeline and you'll see that 4.61 doesn't actually get displayed but the nearest frame shows 4.60
4. Locate to the 4.60 frame and razor blade the clip
5. Now double click the second clip that's just been created and set the Mode to "Static" and the Static Text to "4.61"
6. You'll end up with a counter that stops at 4.61 and you can drag the duration of the second clip shorter or longer depending on how much hold of the static value you want.