Replacing screw terminal
In consumer products, this is achieved with wire-to-wire connectors. You usually buy the connector housing and the contacts separately, and the contacts needs to be crimped to the wire. You can crimp several wires to the same contact to achieve the fan-out you need (to achieve parallel connection, as you call it). Just look at the power supply distribution inside a PC, that's how it is made (with the "molex Y cables"). Take all the wires that should go together, twist them, and crimp them in the same contact. Note that you must always be careful about the min/max AWG size specs of the contact.

Here are a few links to different manufacturers. There is a lot of choice, but for currents such as 45A, there is not many models left actually. You can use multiple pins in parallel to share the current, however.


Molex
JST (with others models available in the automotive section)
Hirose


You can find much more with Google.

Note that you usually need to buy specific tools for crimping the contacts (you can do it with pliers, but then, safety - which seems important to you - will not be guaranteed). But crimping tools cost an arm and a leg. For a DIY project, I'm not sure it is worth it. If I were you, I'd actually just use some heat shrink sleeving around the terminal, after making sure it is very tightly screwed.