I would definitely start by replacing the caps and re-flowing connectors etc first and see where you stand. I believe this cap should work in place of your 160uf/250v, available at GPE: https://www.greatplainselectronics.com/proddetail.asp?prod=CEA-150uF-350V-RMD
The one I listed is a 150uf/350v axial electrolytic cap, which I believe is a suitable replacement. GPE stocks those specifically for early Bally and Stern solid state games. When substituting caps, you can go slightly above or below the capacitance rating, but you always want same voltage rating or higher. In this case, both values are close enough. I'm using those caps on 2 of my games for their HV sections and they originally had 160uf/250v like yours has.
I've found a number of times that the part I'm looking for at GPE won't be in stock there--but they may have a substitute in stock they can recommend. In some cases, the substitute is actually a better choice than the original part. Whatever the case, Ed is a super helpful guy, I'm sure if you have trouble finding a part at his site he'd help you locate it in his inventory.