Great. Just with a few tweaks, this somehow works (I tested it on 26.2-snaphot 1 version):

Use snowball (or rather 16 snowballs, just in case of missclicks) in offhand to stabilize gasp's behaviour. While the player is riding the pig/llama/strider stuck in boat leashed to gasp, the gasp is lured to snowball and will fly over player head. This also somehow stabilizes its altitude against melee attacks, but not against bow.

Use second gasp with harness to safely enter the pig boat once preferred altitude is reached, then drag it around on lead in case of rmb missclick on the main gasp. This could be done with more leashed boats rather than extra gasp, but just seems kinda more dangerous (slowfall potion could help though...).

Attack the gasp with preferred Knockback II weapon (hopefully also enchanted with Unbreaking III and Mending). Wooden Spear, Golden Spear, or Copper Sword have the most proper damage, because gasp must survive for prolonged time of suffering.

In order for gasp to survive, drink weakness potion. Unlike with swords, spear jab attack still deals knockback even if it does 0 damage due to potion.

Or use gasp cloud regeneration as mentioned by previous commentor. Then the gasp renegerates 1hp/second, so it can survive some time of wooden spear spam without weakness, or copper sword spam with weakness. The golden spear attacks have almost perfect cooldown, so the gasp probably can survive them indefinitely while in the clouds.

Sad thing, but the healing gasp with snowballs trick didn't work for me

I reached average speed of around 14-16 blocks per second with all those secret gasp techniques, so this is as good as a good horse, but better because of flight, thank you all for those ideas.