I have figured out how to effectively traverse the galaxy without addressing the absurd distances.
>create strong engines in the Solar system
>accelerate the Sun and it's orbiters near c
>enjoy traversing the galaxy in effectively no observed time
Time dilation will save us eons as instead of dispersing to a whimper, us humans will be stuck with one another but traversing a galaxy together and thus amassing more data relatively fast.
As for the mechanical sides of my project, it will be hard to achieve such speeds and keep the Solar system intact and together. Maybe just accelerate our planet.