Coming up a little short
You can always splice wires, but only inside junction boxes.*
What I would do is put a large steel junction box located so you have ample wire length for your splice (given your short wires). That is to say, don't short-skunk it and leave yourself only 2" of wire inside the box; give yourself a full 9-12".
Then, since the junction box is quite close, connect it to the service panel with EMT, IMC or Rigid conduit. What does this do? That metal conduit is usable as the ground path. Which means you can simply terminate the ground wire right there in the junction box; no need to extend into the panel. Then, in that box, you splice to extend the neutral wire. The last segment through the metal conduit only has 3 wires in the pipe.
I actually do this intentionally, in almost all my circuits. The reason is, I acquired a factory building where breaker thieves had cut all the wires at the edge of the panels. So I simply installed a bunch of boxes <24" up the conduits and spliced there. The splices have given zero trouble. They also let me transition from legacy solid wire to stranded wire for easy working in the panel. So I'm a fan of the technique, and even use it in places I don't need to -- they're a great place to stick $16 GFCI receptacles or deadfronts instead of $40 GFCI breakers.
Busy grounds in boxes
Remember ground wires are almost free in conduit fill calcs; you count only the largest wire once.
First, if you have a metal junction box, and your receptacle also has a metal yoke, and the receptacle sits hard-flush onto the metal screw-mounts on the junction box -- no gap, rust or little paper squares in the way -- then the receptacle grounds through this hard yoke-box contact. So you don't need a recep-box jumper wire. That frees up the ground screw on the junction box for your supply cable.
Or, you can drill multiple #10-32 holes in the junction box and have multiple ground screws. Legit!
Or, if you're really vexed by the need to ground multiple wires to the box frame, you can pigtail.
If that's too much for you (e.g. you are using #6 wire), then here's a cheat -- shop for "accessory ground bars" for service panels. Some are only 3" long and will fit nicely inside a junction box. Attach them flush (drill and tap a couple #10-32 holes if needed to mount them; don't put screw holes in removable knockouts). Then attach to the lug holes on the bar. That will slickly deal with #6 wire and aluminum wire, since they are aluminum rated.
* Or conduit bodies so large that they have sufficient cubic inches to qualify under the junction-box rules; however this may foreclose adding any more circuits to the conduit.)