Take a close close look at the latch relays, such as the game over relay. There is very little travel on these and they are quite easy to get out of adjustment and cause the sorts of problems you face. Also unless the game kicks the ball out and closes the switch as it rolls towards the plunger the game won't behave properly.
Setting the game to free play is really easy. When the credit reel reads 0 you will see two switches open, when the reel reads 1 or more those switches close. Either bend them so they are always closed or put a jumper wire on the one that allows the game to start. Beats me which one that is, but if it isn't the first one its the second (the other switch is to stop the credit reel from trying to go below 0 I think, nut sure as the reel usually has a mechanical stop to prevent it from doing that. You can jumper each one separately but only one needs to be closed to have the game work on free play). Then nice thing is that credits will still go up and down as you win games, pay for games and play games. It just lets you play more once you get down to 0.
Good luck.
I hope to get Target Alpha up and running in the basement this weekend.