Glitchy Characters on Overworld Chocobo

The low byte of the sprite address is in $6A, middle byte in $6B and high byte in $6C. The only solution I see is adding an exception before EE/8980 where you check the offset and change it in case it match the offset of your character riding sprite. Let's take Terra's example and assume she has a riding sprite at F0/6820. Her default riding sprite is at D5/0180.

Code:

01) LDA $6A     (load calculated low byte)
02) CMP #$80    (compare loaded low byte to expected one)
03) BNE  $????  (branch to step 16 if it doesn't match)
04) LDA $6B     (load calculated middle byte)
05) CMP #$01    (compare loaded middle byte to expected one)
06) BNE  $????  (branch to step 16 if it doesn't match)
07) LDA $6C     (load calculated high byte)
08) CMP #$D5    (compare loaded high byte to expected one)
09) BNE $????   (branch to step 16 if it doesn't match)
10) LDA #$20    (we are here if the whole offset match the expected one)
11) STA $6A     (store new low byte)
12) LDA #$68
13) STA $6B     (store new middle byte)
14) LDA #$F0
15) STA $6C     (store new high byte)
16) Normal code at EE/8980

That would only be good for one character though. You would have to do a check for each character that has a riding sprite in the extended data, unless there is some order there which would allow to develop a calculation logic.

Edit: The other option would branch on the sprite ID and add a calculation logic for sprite IDs higher than 15.