Hello David,
I think the following schedule will work for your tournament. It has a cyclic structure where each column loops round the players A to K, or L to V.
(N Q v H A) (L R v T M) (U C v B J) (P G v I D) (K S v O E) (V F)
(O R v I B) (M S v U N) (V D v C K) (Q H v J E) (A T v P F) (L G)
(P S v J C) (N T v V O) (L E v D A) (R I v K F) (B U v Q G) (M H)
(Q T v K D) (O U v L P) (M F v E B) (S J v A G) (C V v R H) (N I)
(R U v A E) (P V v M Q) (N G v F C) (T K v B H) (D L v S I) (O J)
(S V v B F) (Q L v N R) (O H v G D) (U A v C I) (E M v T J) (P K)
(T L v C G) (R M v O S) (P I v H E) (V B v D J) (F N v U K) (Q A)
(U M v D H) (S N v P T) (Q J v I F) (L C v E K) (G O v V A) (R B)
(V N v E I) (T O v Q U) (R K v J G) (M D v F A) (H P v L B) (S C)
(L O v F J) (U P v R V) (S A v K H) (N E v G B) (I Q v M C) (T D)
(M P v G K) (V Q v S L) (T B v A I) (O F v H C) (J R v N D) (U E)
A player's 10 partners are all different, and a player's 20 opponents are all different. Also the single player who is not seen in opposition, is one of the 10 partners, so the schedule has the optimal social mixing property that you are looking for.
Hope the tournament is a success.
Ian.