If you're just comparing your team to one other team and want to do it at any point on a course, just spot head to head battles. Count if your #1 is ahead of their #1, your #2 is ahead of their #2, etc.
Chances are if you are beating them in three or more out of the five scoring spots, you're beating them. Obviously this is not foolproof, but most days I find that it works if the teams are pretty comparable to begin with.
Things get skewed when you have a team that is great at #1 - 3, but their 4th and 5th are pretty bad and inflate the team score a lot at big meets.
To score a state meet...that's a different ball game...
Stand near the finish or just outside the chute, and record finish places for just the teams you are concerned about. We normally are in the top 4 at our state meet, and so I really only have to worry about scoring 3 - 6 teams each year. I'll only worry about writing down those team's runners finishing places, and disregard the teams that won't be in the mix. I leave blanks for the teams that aren't in the mix. It's still not perfect, because you'll have individuals not on a team that displace runners in this case. It's easy for the first 10 - 20 runners, but then gets pretty hectic. Always good to have some JV runners at your side just counting one team and telling you as you write down. I usually score the girls meet for our girls coach this way, and then they score the boys meet out.