Substitution question

[DownTownTonyBrown]

OBR only (no FED - I understand the FED)

Batting order for Team Alphanumeric is as follows:
1. Alpha - F2
2. Bravo - F3
3. Charlie - F4
4. Delta - DH
5. Echo - F5
6. Foxtrot - F6
7. Golf - F7
8. Hotel - F8
9. India - F9
10. Juliet - F1 (not batting)

In the 6th inning with Team Alphanumeric on defense...

F1, Juliet, moves to F8 and enters the batting order in the 8th position (He previously has not been batting due to the DH role).

F9, India, is now going to pitch. DH, Delta, goes to position F9 and plays right field.

DH role is now terminated (because F1, Juliet, has left the pitching position and moved to a different defensive position) - DH, Delta, must now play defense. And one of the defensive players (India) must leave his defensive position and the batting order.

The batting order for Team Alpha numeric now becomes:

1. Alpha - F2
2. Bravo - F3
3. Charlie - F4
4. Delta - F9
5. Echo - F5
6. Foxtrot - F6
7. Golf - F7
8. Juliet - F8
9. India - F1

Previous #8 batter, Hotel, is now out of the game and cannot re-enter (no re-entry rule in OBR).

This is allowed, correct? This is per the requirements of the rule as stated "The DH may be used defensively, continuing to bat in the same position in the batting order, but the pitcher must then bat in the place of the substituted defensive player,... (and) Once the game pitcher is switched from the mound to a defensive position this move shall terminate the DH role for the remainder of the game... (and) Once a DH assumes a defensive position this move shall terninate the DH role for the remainder of the game."

And this change can only be made with Team Alphanumeric on defense, per the parenthetical portion of the rule "(The game pitcher may only pinch hit [and this portion of the rule is extended to also mean pinch run] for the DH.)"

Is this all correct?