Here's one with 6: РڠໃמୡඤVŦலڄໃݲథɊІށ௨ಘQɕ௫ҨໃυɷඞМǶ௨ళɱݹ୦Οຯ൫௩ƦഫJமϺຽߢ௧uܘܭЬ௨൧ݹಈඤʆٻҳචHݹಏටฅکҿࡄแחजலາƷ௧οາঐ௧চІͷ௨ౚໃŧԥఠܕɕϢ෯ƚݢƐٮඍԣரಀԀສߜƣƬѣݫΝթֆଔ

I suspect that there's some pathological behavior in the game you can exploit to possibly get a line or more while giving up a line (not that I searched and identified one, I think I just got lucky on my second game because I don't play tetris much so didn't have much of a strategy to unlearn). It would be interesting if there a few of these behaviors that lead into each other, which could lead to a stable state of infinite lines.

Not being random means there might be more to exploit.

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

8: ౚටරଳ௨ಗҾђञఢІŦଛقࠂɜ௨ఢVʣƃڠࠃʦذਓງஈ௧vഫݹযуಮɜटطϼƷ౻ඝЈஈ௩ΣܘŦ૧ට๒ݹଢඈฆŧذࡄɱݸϢరμŦௐؼVϳ௧৩ะݹ௨૫ຣ૨ரڴТߣ௧ڒІŒɷഗƖԤݛஶՀݮ൙൶ຯݷ౧Փຯబ௩ʡWђƓעXݪݖضɑЈԎϺثॿƖ੪СجƕןÞڍ۰Ռ

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

small improvement to your solution, 9: సقໂɜ௨ഗƊݺɷටЖݹযמຽঅ௧ปໃঅਓsຯɜ௧ࡆଈŧԥටȤ൫௧ڈໃܘ௨කІԾ௨ඝІԘ௨ಳଈݰ௨൲ຣݹஜɦܗɚ௧ปลഴஐٯүݚ௩ظݕܥ౫ಀۻࡨஶԛɒঅਏڏІŧۑڐසђߥѲಊݷѻइࢳݪޜപࡊ०ணගɛܡ౦ಬҾɚ౫ఢʂډױ3

this one is pretty brilliant

Another 6: ఢ૫ໃυޛඞਖࡨௐงເƍ౫൶ลٽ௨౾ІJ௮ටСݺԊق໐ɞ௨൜షݸ౻ටܬݹԪࡄถࡨ௭ඞФॡஸػʒஆಒ෩ಸݹࢳටଜݶౚ൜ਈމ௧෬ІھƐೲໄߢসࡆІݚɷ൜ປ൴ƋٯຯРமҔПܢமɈܢܭԤڌฅٽߤఏە

Agree it is like chess.

The world record from 2017 is 31. "௨ഖƌݯߜࠏІWƑsໃa௨೯ܘݷಳජଈیԪؼʥݺԥඞܘݲࠐڄໂঅமةໃݹ௧ړІٽ௨൞ໃZ௨ಘІܥࠐΣІZߜටȜখذජНݹߛeʛݹߤปເѧ௩ԚໂՉࢸටuа௨સȣݷłقෆঅਏeܘԔצقషݸɢڠຜঀಧҸມѧஐට༪൩ԊಅഫܡथsถԡԦԚໃɥஸقࡈɕɠɈไݸצقషݰਵϺФঅஓػݐɓԞуຯɕझࡈ๐ݞझࢶІݞमปദஈƉؿଭݪஸҩЂ൸ԛمϦGƁҨVھԥචЅշࡂ෮लݷƘණ໘ࠅƘಧНקࢻҨฆӘದԋϝପࠑ੧ͳݲடփරݞਵΚϼɢԒԺٳѦԤࠌξGಘسਯܥஶҋϮτथlϼʔ"

Astonishing! I love it.

I managed to get 5: ௬চІݪݹටຽࠇ௨රІݪشॴເເƕؿ٠ܥ౻ഡϿߢ௧กȤڥƐඨɱݺƔقහݹࠉඦТ൫௮ࡄරࢲԥට༥ݹࠔقฮݹஓپଈKƐൽЫݚɷಪІݎ౫ඨIƬޛගƸݰಏஶເםݮقไࡨறۊసໃ௧Οࠕࠄېୱ೦ݶћؾƔݷɘ੬ÐԴযϺƛԾతࡕ

I managed 7: ౚටໃࡈ௧ࡆໃށɷಘƬݎసغƔܭɷටܤݹઽॴແࠇభගÐҲƏڠໃק௨хଈݪƐڠຈݚ୶ටງங௨ඉʃݹலڌໃए௨ڐໃऍ௩Ѯ༩ކѲƤЈஈ௧څȣݺޔلໄєذ൝ܘɡ௰ࢲДם୦ΟଠܭݗॵÐࢣ௮ඪ

That was a fun watch. You're really good at this!

Absolutely love the playback feature.