The proper way to install is with a tool , it will thread into the front of the crank & has a nut & torrington brg to push the damper on .
Yes you can gently tap the damper on a little & use the bolt to tighten it , I would want at least 3/8 " of thread engagement to start , Lube the threads of course . Warning tho this can damage the #3 crank brg which is the thrust brg so if it will not go on easily use a tool to press it on .
I cannot see the front of the damper , there are a lot of different dampers , , you have neutral balance with a steel crank , you have the HP damper used for 6 pack rods & steel crank which has an offset balance , you have the cast crank damper which is offset balance , All 3 are different so the ones with offset balance are not the same so you need to know exactly what you have to get the correct replacement , Mancini racing should be able to help .
The 3 holes drilled in the rear of your balancer could be for the 6 pack BTW