Are there game specific jumpers or 0 ohm resistors that you would need to change between the two?

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Sounds like a switch issue. BK needs three perfectly working lock switches up top and three perfectly working lower trough switches to work properly. If they aren't working properly, the game gets confused.

Pop all the drops up, remove the balls, and go into the switch test. All switches should be open at this point. Roll a ball into the lower trough and make sure the first trough switch works. Then roll a second ball in and make sure both trough switches are working. Then add the third ball and make sure all 3 are working and staying closed. Now, reach under the playfield and activate shooter lane eject throwing a ball into the shooter lane. Now make sure the first two trough switches and the shooter lane and staying closed. Then take the ball from the shooter lane and put it into the top lock, making sure all 3 switches are registering. Then take another ball from the lower trough and put it into the top lock, making sure all 3 switches close. Take the final ball from the lower trough and place in the top lock, making sure all 3 top switches are registering.

The manual may have the same jumper info, but did you actually look at the board to confirm it is jumpered correctly?
Also, what is adjustment 37 set to? I dont know what the conservative multiball settings are for bk.