The suggested changes to the summoning rule seem overly complicated to me. I would suggest instead making the summoned pieces switch sides when captured, like shogi pieces. Then the players would want to be careful about losing the demon, since that would allow the opponent to summon it later. If you want losing a summoner to be more consequential, a captured demon could only switch sides if the capturing player still has the right piece to summon it back.
The suggested changes to the summoning rule seem overly complicated to me. I would suggest instead making the summoned pieces switch sides when captured, like shogi pieces. Then the players would want to be careful about losing the demon, since that would allow the opponent to summon it later. If you want losing a summoner to be more consequential, a captured demon could only switch sides if the capturing player still has the right piece to summon it back.