Before jumping to a new Galaxy, Pack the modules and place them on the inventory, switch the multi-tool to a crapy C-class one and use a ship with no mudules installed.

Once you jumped, re-install everything, with very little left to repair.

Yeah, it's beneficial to uninstall your technology before jumping through the core. Having spare multitools & ships also helps :)

FYI your entry point into the next galaxy is derived from your last black hole jump.

So, find a black hole within the inner 1000LY ring/sector of the galaxy and jump through it, then jump to the centre. You'll arrive in the new galaxy at more or less the same distance from the centre as you exited the black hole.

For bonus points, plonk a base down or visit a space station so you can use the transporter to jump back to any galaxy you've visited.