What helps against astringent mouthfeel from spinach or chard?
Blanching briefly does an excellent job of neutralizing bitterness, or more precisely, astringency, even if the blanched spinach is recooked.

Basically, boil water, add washed spinach until submerged (5-30 seconds depending on preference; chard could go up to a minute or so depending on the target texture desired). Drain quickly. Submerge drained spinach in a bowl of ice and water to rapidly chill. Press spinach to remove excess water.

Recooking, even in applications like quiche, will do a very nice job of retaining the bright green color and generally astringency, if present at all, is minimal. If I am not recooking in some way, I often just dress simply in something like fresh ginger and soy sauce or a ground sesame, mirin and salt based sauce without reheating.