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In any setting with computers, someone is eventually going to want to hack them. Realistic computer hacking is probably the single most boring thing in the world to roleplay, so you need to abstract it and make it interesting somehow.
One cool way is to take inspiration from the cyberpunk genre: Treat computer hacking as entering a virtual world of cyberspace, in which you have encounters with deadly software. Several game systems have described rules for doing this: Cyberpunk (various editions subtitled 2020/V3.0/RED) and GURPS Cyberpunk in particular.
Lacking these, you can just drop the neurally interfaced netrunning characters into a completely different genre using different game rules! Just say it's a computer simulation of a pseudo-medieval fantasy world, or an Age of Piracy swashbuckling adventure, or whatever.
Commentary by memnarch (who has not seen the movie)
Oooooh. Now that gives me an interesting idea. Never mind on the "continue running away" plan; what if the Resistance turns the Raddus around and instead of abandoning ship and using it as an unguided missile, they use the Raddus as the largest boarding vessel ever? A suicide dive with the ship isn't really heroic, but ramping up their forward shields to breach the enemy's defences and try and take over a different ship? That'd be heroic and cool enough to possibly work. At the very least, that would allow them to take over smaller ships inside that could allow them to run away better in the confusion.
And if BB, DJ, Finn, and Rose can pull off the same boarding maneuver onto another First Order ship (Snoke's as mentioned perhaps), that could make that idea work even better! BB-8 could hack the fleet data to make all of the First Order ships register as both friend and foe, and maybe even mess with the communications too. Being unable to trust their sensors or talk would cause so much confusion about which First Order ships are piloted by the Resistance and escaping the Raddus-attacked star destroyer. Sure, there's the whole timing problem of the group leaving in the chase, having casino events, then coming back in time, but weird timing isn't new to Star Wars (in Episode V no less!) so that could still work out.
Transcript
Finn: Poe! Don’t go getting any reckless ideas.
Poe: Those are the best ideas!
Finn: Rose, we gotta do something!
Rose: Look, Poe, give us a chance to complete our part of the plan.
BB-8: What’s to complete?
Rose: If we can hack into the First Order’s computers directly and just... insert enough orders, then they’ll have to redirect their fleet like we planned.
BB-8: But to do that we’d need to be on a First Order ship.
Rose: We infiltrate Snoke’s ship!
DJ: I like it!
Finn: How are we going to do that? They must have security up the wazoo.
DJ: I can do it.
Finn: So you’re going to be reckless and not Poe?
DJ: Cur non utrumque?