There are standard Whist schedules for 4n+1 players which are perfectly balanced. These have all partners once, all opponents twice, each player plays in 4n rounds and has 1 bye round. So 9 & 13 from your list above are easy to handle. I will cover 11 & 15 players later.
5 Players & 5 Rounds
(B E) v (C D) (A)
(C A) v (D E) (B)
(D B) v (E A) (C)
(E C) v (A B) (D)
(A D) v (B C) (E)
9 Players & 9 Rounds
(B C) v (D G) (E I) v (F H) (A)
(C A) v (E H) (F G) v (D I) (B)
(A B) v (F I) (D H) v (E G) (C)
(E F) v (G A) (H C) v (I B) (D)
(F D) v (H B) (I A) v (G C) (E)
(D E) v (I C) (G B) v (H A) (F)
(H I) v (A D) (B F) v (C E) (G)
(I G) v (B E) (C D) v (A F) (H)
(G H) v (C F) (A E) v (B D) (I)
13 Players & 13 Rounds
(B M) v (I F) (C L) v (D K) (E J) v (G H) (A)
(C A) v (J G) (D M) v (E L) (F K) v (H I) (B)
(D B) v (K H) (E A) v (F M) (G L) v (I J) (C)
(E C) v (L I) (F B) v (G A) (H M) v (J K) (D)
(F D) v (M J) (G C) v (H B) (I A) v (K L) (E)
(G E) v (A K) (H D) v (I C) (J B) v (L M) (F)
(H F) v (B L) (I E) v (J D) (K C) v (M A) (G)
(I G) v (C M) (J F) v (K E) (L D) v (A B) (H)
(J H) v (D A) (K G) v (L F) (M E) v (B C) (I)
(K I) v (E B) (L H) v (M G) (A F) v (C D) (J)
(L J) v (F C) (M I) v (A H) (B G) v (D E) (K)
(M K) v (G D) (A J) v (B I) (C H) v (E F) (L)
(A L) v (H E) (B K) v (C J) (D I) v (F G) (M)
17 Players & 17 Rounds
(B Q) v (N E) (D O) v (F M) (J I) v (P C) (K H) v (L G) (A)
(C A) v (O F) (E P) v (G N) (K J) v (Q D) (L I) v (M H) (B)
(D B) v (P G) (F Q) v (H O) (L K) v (A E) (M J) v (N I) (C)
(E C) v (Q H) (G A) v (I P) (M L) v (B F) (N K) v (O J) (D)
(F D) v (A I) (H B) v (J Q) (N M) v (C G) (O L) v (P K) (E)
(G E) v (B J) (I C) v (K A) (O N) v (D H) (P M) v (Q L) (F)
(H F) v (C K) (J D) v (L B) (P O) v (E I) (Q N) v (A M) (G)
(I G) v (D L) (K E) v (M C) (Q P) v (F J) (A O) v (B N) (H)
(J H) v (E M) (L F) v (N D) (A Q) v (G K) (B P) v (C O) (I)
(K I) v (F N) (M G) v (O E) (B A) v (H L) (C Q) v (D P) (J)
(L J) v (G O) (N H) v (P F) (C B) v (I M) (D A) v (E Q) (K)
(M K) v (H P) (O I) v (Q G) (D C) v (J N) (E B) v (F A) (L)
(N L) v (I Q) (P J) v (A H) (E D) v (K O) (F C) v (G B) (M)
(O M) v (J A) (Q K) v (B I) (F E) v (L P) (G D) v (H C) (N)
(P N) v (K B) (A L) v (C J) (G F) v (M Q) (H E) v (I D) (O)
(Q O) v (L C) (B M) v (D K) (H G) v (N A) (I F) v (J E) (P)
(A P) v (M D) (C N) v (E L) (I H) v (O B) (J G) v (K F) (Q)
21 Players & 21 Rounds
(B C) v (M P) (F D) v (G S) (E L) v (H U) (I T) v (N R) (O J) v (K Q) (A)
(C D) v (N Q) (G E) v (H T) (F M) v (I A) (J U) v (O S) (P K) v (L R) (B)
(D E) v (O R) (H F) v (I U) (G N) v (J B) (K A) v (P T) (Q L) v (M S) (C)
(E F) v (P S) (I G) v (J A) (H O) v (K C) (L B) v (Q U) (R M) v (N T) (D)
(F G) v (Q T) (J H) v (K B) (I P) v (L D) (M C) v (R A) (S N) v (O U) (E)
(G H) v (R U) (K I) v (L C) (J Q) v (M E) (N D) v (S B) (T O) v (P A) (F)
(H I) v (S A) (L J) v (M D) (K R) v (N F) (O E) v (T C) (U P) v (Q B) (G)
(I J) v (T B) (M K) v (N E) (L S) v (O G) (P F) v (U D) (A Q) v (R C) (H)
(J K) v (U C) (N L) v (O F) (M T) v (P H) (Q G) v (A E) (B R) v (S D) (I)
(K L) v (A D) (O M) v (P G) (N U) v (Q I) (R H) v (B F) (C S) v (T E) (J)
(L M) v (B E) (P N) v (Q H) (O A) v (R J) (S I) v (C G) (D T) v (U F) (K)
(M N) v (C F) (Q O) v (R I) (P B) v (S K) (T J) v (D H) (E U) v (A G) (L)
(N O) v (D G) (R P) v (S J) (Q C) v (T L) (U K) v (E I) (F A) v (B H) (M)
(O P) v (E H) (S Q) v (T K) (R D) v (U M) (A L) v (F J) (G B) v (C I) (N)
(P Q) v (F I) (T R) v (U L) (S E) v (A N) (B M) v (G K) (H C) v (D J) (O)
(Q R) v (G J) (U S) v (A M) (T F) v (B O) (C N) v (H L) (I D) v (E K) (P)
(R S) v (H K) (A T) v (B N) (U G) v (C P) (D O) v (I M) (J E) v (F L) (Q)
(S T) v (I L) (B U) v (C O) (A H) v (D Q) (E P) v (J N) (K F) v (G M) (R)
(T U) v (J M) (C A) v (D P) (B I) v (E R) (F Q) v (K O) (L G) v (H N) (S)
(U A) v (K N) (D B) v (E Q) (C J) v (F S) (G R) v (L P) (M H) v (I O) (T)
(A B) v (L O) (E C) v (F R) (D K) v (G T) (H S) v (M Q) (N I) v (J P) (U)
With 11 players and 3 byes per round, it is probably best to go for 11 rounds, so that each player gets exactly 8 games and three bye rounds. It's possible to arrange this, so each player has 8 different partners and sees all other players as opponents either once or twice. Below the byes are nicely separated, with at least two rounds of play between between byes.
11 players & 11 rounds:
(I G v E J) (B F v K C) (D H A)
(J H v F K) (C G v A D) (E I B)
(K I v G A) (D H v B E) (F J C)
(A J v H B) (E I v C F) (G K D)
(B K v I C) (F J v D G) (H A E)
(C A v J D) (G K v E H) (I B F)
(D B v K E) (H A v F I) (J C G)
(E C v A F) (I B v G J) (K D H)
(F D v B G) (J C v H K) (A E I)
(G E v C H) (K D v I A) (B F J)
(H F v D I) (A E v J B) (C G K)
With 15 players, any multiple of 5 rounds would be a sensible choice. Below I give an example with 15 rounds, where each player has 12 games, 12 different partners and, all other players as opponents either once or twice. Players have one bye in the first 5 rounds, one bye in rounds 6 to 10, and one bye in the last five rounds.
(B G v E I) (A M v F J) (K O v L D) (C H N)
(C H v A J) (B N v G F) (L K v M E) (D I O)
(D I v B F) (C O v H G) (M L v N A) (E J K)
(E J v C G) (D K v I H) (N M v O B) (A F L)
(A F v D H) (E L v J I) (O N v K C) (B G M)
(O L v A I) (B D v J N) (M F v E G) (C H K)
(K M v B J) (C E v F O) (N G v A H) (D I L)
(L N v C F) (D A v G K) (O H v B I) (E J M)
(M O v D G) (E B v H L) (K I v C J) (A F N)
(N K v E H) (A C v I M) (L J v D F) (B G O)
(H N v D M) (O E v A B) (G I v K F) (L J C)
(I O v E N) (K A v B C) (H J v L G) (M F D)
(J K v A O) (L B v C D) (I F v M H) (N G E)
(F L v B K) (M C v D E) (J G v N I) (O H A)
(G M v C L) (N D v E A) (F H v O J) (K I B)
I hope your Euchre group finds these schedules useful.
Ian.
For the benefit of other readers here are some links to other schedules on this message board relating to doubles play:
7 players 7 rounds
10 players 10 rounds
10 players 15 rounds
14 players 14 rounds
18 players 18 rounds
20 players 10 rounds
22 players 22 rounds
24 players 10 rounds
24 players 12 rounds
For fully balanced schedules involving 4n players then click on the schedules link near the top of this page and select "Whist" and the number of players to display a suitable schedule.