This was new to me
 

FED rules. The DH (who is batting for the pitcher) reaches base. The offensive coach enters the pitcher to run for the DH. After one pitch, the coach requests a courtesy runner for his pitcher. Can he do this? Some of you might say, "Why not just put in the runner for the DH and be done with it?" If he did that, he would no longer have the runner as a legal substitute later in the game.

What does everybody think?

Yes, coach may use a courtesy runner, but the role of DH is eliminated by pinch running the defensive player (the pitcher in this case) for the DH.

Rule 3-1-4:

No problems at all ... until he tries to have that DH bat the next time around. In fact, as opposing coach, I wouldn't say a peep (although I'd surely watch to see that the umpire was making some notation when the pitcher came in to run)... until that DH came back to bat.

Most opposing coaches (rats) wouldn't have any idea about the correct ruling on the substitution.:D

Most rules, I agree with you. THIS one, however, is similar enough to MLB that most people who have watched baseball on TV will know that if the pitcher goes in, the DH is gone.

Re-Entry
 

As a starting player, doesn't the DH get one re-entry. He can simply re-enter when his spot in the batting order comes up next time. Then the pitcher can re-enter to take the field the next inning.

Yes, the DH gets one re-entry, UNLESS the defensive player for whom he bats pinch runs or hits for him. See the rule I posted in post #2 above.

Just look at it like this. With a DH it is like having ten starters. However the DH and the person being DH for cannot be in the field at the same time. If the DH comes back into the game in the above situation, he replaces the person he DH for or the replacement for the person who was DH for.

This would be easy to deal with here...there is no courtesy runner for pitchers...just catchers.

Even easier in Portland, where, I believe, there are no courtesy runners for anyone.

Yep,
 

Since this is a NFHS question the following statement is correct:

"Even easier in Portland, where, I believe, there are no courtesy runners for anyone."

And I feel rather odd since I have no knowledge of CR rules and regualtions.

Regards,

Role
 

The ROLE of the designated hitter is terminated for the remainder of the game when:
a. the defensive player, or any previous defensive player for whom the designated hitter batted, subsequently bats, pinch-hits or pinch-runs for the designated hitter

I know that he cannot re-enter as the DH, but as a starting player he can re-enter the game. He would simply be a pinch-hitter and not the DH.

The CR rules are posted behind Rule 10 in FED rulebook. They are adopted in my state. The AFTER PUTOUTS rules are not.

These are meant to be speed up rules but it is my observation that it slows the game vs. speeding it up. For many teams a pitcher an infielder brings hat and glove to he pitcher who was on base when the last out was made. For the catcher it usually takes more time to run a player on and run the catcher off than it does for the catcher to get ready when he was the last batter. Many teams will send a player out to warmup the pitcher while the catcher gets ready.

No, the player who was the DH can reenter. The role of the DH is terminated but his eligibility is not.

Right, the player gets a re-entry, but not as DH. Sorry for the misleading phrasing.