You need to step through the audits in self test and clear out each and every one.
Press the self test button 6 times to get past the self tests and into the first audit.
Press the button next to the self test to clear the entry, '00' should be displayed in player 1 display.
The first 3 audit entries are the replay scores. After clearing, you can hold in the credit button to set the score at the desired level, then press the self test button to step to the next one.
Step through the remaining entries, clearing each one.
The game will reboot once you've stepped through all of them.

Check MPU switches 15 and 16. If both are off the high game to date feature is disabled. I've never disabled the feature on any of my games, so I have no idea whether or not it still displays the high score.

mpu200 stern games it does not. 15/16 are just for the # of credits, setting to 0 credits still has hstd going. gottlieb and wms games I think will disable showing it though.

There might be a bug in the version of 9 ball regarding the hstd. Sometimes it cycles and sometimes it doesn't. I'll look at it in the future and see if I can determine what's wrong with that.

UPDATE: So I'm testing the version v21 in pinmame, and I can't get the hstd to not show at bootup, but it won't cycle the last scores. I'll have to try and play a game virtually to see what happens at the end of the game. There was an issue with the quicksilver software and this but that was concerning the matching being off/on. Do you happen to have match on in case it turns out to be a similar thing?

ok, I just tested both ways in pinmame, there is an error in processing at bootup - it will only show the hstd on the displays. After the game is played, it works fine. (if match is on or off). So, this is the opposite of what you're seeing, which is strange. The hstd lamp does cycle on and off at the end of the game as its supposed to, and it's lit on the stuck hstd at bootup as well. I will likely redo it so it cycles at bootup since it's supposed to do that, but I don't get why you're getting the opposite of what the stuck routine is here.

here's the code snippet.... it's actually something that didn't get changed in 9 ball, (unlike quicksilver, which had much tighter code):
swi ; start pigs
rcflagset ; set pigs multiprocessing flag
lampbvalueon $32 ; game over
show_credits ; get credits on display
show_hstd ; get hstd on all 4 displays
update_match ; do match/game over

So the show hstd routine does key off having the game over lamp lit, (at least on quicksilver it did, which was the bug).

I think likely what's going on so it's not cycling is that the timer for it is not getting set so I'll double check that.

hmmm.... I'm looking deeper into this, this is one game I didn't really optimize/cut out things from the code to shoehorn the fixes in. So most of it is the stock stern code. Between the original code and the mod, there's an added routine that's not in other games that is responsible for doing the single saucer eject in the stock game added into the hstd display routine. I'm not using that but it's still in the new code, I think it's there so that if you try and start a game without all the balls, it sets a flag which this routine reacts to to just eject the saucer (regardless if a ball is in it or not).

I also use this routine but I check the saucer switch and eject it if its closed as the new software puts all the balls in the trough, no ball carryover. I will excise the routine that was originally there and it should solve your non-cycling display issue.

uploaded v22 with this change to http://tsqmadness.com/slochar/ZIP/ if you want to give it a try, versions for weebly, 716, 732 included.

Usually you have to reburn all unless otherwise stated. The file has different formats but you burn all the ones labeled for your chip type. 2 for 2732, 4 for 2716 and one if you have weebly 512.

Did it show new version number in match display at bootup?

What does adjustment 4 show? If it's all blank hit clear on the door or S33 on the mpu. It should then show 00.

Wouldn't surprise me I have no way to test it. I'll get rid of v22 off the website and leave 21 as the latest version until I can play around some more.

Not sure if it helps as confirmation but in MAME, V22 in attract mode with credits won't start a game. Swap in V21 ROMs and game can start.

Yeah, the errant routine has a credit button flag at its start which I thought was just used in the original code to eject the lock saucer at bootup... apparently not.