Gaping Gill is a system, there's a lot of entrances. Potentially that could mean a lot of things. Given that most routes would involve >=2 pitches and aren't really condusive to pull through, through trips would be limited.
AFAIK, you've got 2 options really
1) winch meet. Go on one of the 2 winch meet weekends, like the one coming up
https://www.cravenpotholeclub.org/index.php/about-gaping-gill/visit-gaping-gill and see if you can in through a pre rigged route and out through a pre rigged route (or winch out if available)
2) An exchange trip with another party, there's a heap of options for that. The two most popular routes for doing that could be Main Hang - *Dihedral*
https://cncc.org.uk/cave/gaping-gill
and Bar Pot
https://cncc.org.uk/cave/bar-pot
Whichever party exits via Dihedral has got to be good for jumaring 2*55m and while dangling in free space in very grand surroundings.
The start of bar pot (first 2 or 3m of the first pitch) is a bit "marmite". Personally I find it enjoyable and sporting entertainment but it rubs some people up the wrong way. I weigh 75-78kg and fine but you wouldn't want to be bigger for sure!
If you can exchange trip... Dihedral/Bar Pot would be a day out to remember (one way or the other

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Edit: because this is readable by anyone on the internet, better add a disclaimer that the description above is for competent SRT people only! And not somewhere to learn new skills.
Edit2: Lost river is a brilliant film, available on YouTube. RIP Sid Perou, recently passed away.