[salmonellaeater]

Yeah you can game it to fill in upper levels because it seems to greedily avoid letting you complete the next 1 row.

Here's a game with 7:

ԫقຽࡨதقลƻஸปໃɡЩටʈम౻ටիঅஶΟໃࡦѻ೯ܘݪ௨൜ІݚɪؾÐݪߜගІסञඉȣݣ౫ඞУݸԫؼПݒ౺sܪݚஶsԀŦਛfΔݹटɈເљࠑಜÐݶɺටळ൪ԪؾЂɚலڌෆࡨࢸదQॡభඝଘݒಈలНމࢲඖИܭޜϻϨॷభĐ

[b3orn]

8: ౚටරଳ௨ಗҾђञఢІŦଛقࠂɜ௨ఢVʣƃڠࠃʦذਓງஈ௧vഫݹযуಮɜटطϼƷ౻ඝЈஈ௩ΣܘŦ૧ට๒ݹଢඈฆŧذࡄɱݸϢరμŦௐؼVϳ௧৩ะݹ௨૫ຣ૨ரڴТߣ௧ڒІŒɷഗƖԤݛஶՀݮ൙൶ຯݷ౧Փຯబ௩ʡWђƓעXݪݖضɑЈԎϺثॿƖ੪СجƕןÞڍ۰Ռ

[kbenson]

A little searching and I found this: https://tetris.fandom.com/wiki/Hatetris#High_score which includes a replay for a high score of 31, which I've added below.

31: ௨ഖƌݯߜࠏІWƑsໃa௨೯ܘݷಳජଈیԪؼʥݺԥඞܘݲࠐڄໂঅமةໃݹ௧ړІٽ௨൞ໃZ௨ಘІܥࠐΣІZߜටȜখذජНݹߛeʛݹߤปເѧ௩ԚໂՉࢸටuа௨સȣݷłقෆঅਏeܘԔצقషݸɢڠຜঀಧҸມѧஐට༪൩ԊಅഫܡथsถԡԦԚໃɥஸقࡈɕɠɈไݸצقషݰਵϺФঅஓػݐɓԞуຯɕझࡈ๐ݞझࢶІݞमปദஈƉؿଭݪஸҩЂ൸ԛمϦGƁҨVھԥචЅշࡂ෮लݷƘණ໘ࠅƘಧНקࢻҨฆӘದԋϝପࠑ੧ͳݲடփරݞਵΚϼɢԒԺٳѦԤࠌξGಘسਯܥஶҋϮτथlϼʔ

[altvali]

small improvement to your solution, 9: సقໂɜ௨ഗƊݺɷටЖݹযמຽঅ௧ปໃঅਓsຯɜ௧ࡆଈŧԥටȤ൫௧ڈໃܘ௨කІԾ௨ඝІԘ௨ಳଈݰ௨൲ຣݹஜɦܗɚ௧ปลഴஐٯүݚ௩ظݕܥ౫ಀۻࡨஶԛɒঅਏڏІŧۑڐසђߥѲಊݷѻइࢳݪޜപࡊ०ணගɛܡ౦ಬҾɚ౫ఢʂډױ3

[barkingcat]

this one is pretty brilliant