Sorry to hear that... I know first hand how annoying that is!
I suspect that the Yamahas are using a similar (non-standard) 1/4" jack like the 2 conductor mono jack to what Ernie Ball uses on Stingray basses.
I actually had a gig last weekend and I was able to successfully use the right angle jack that Line6 provides with the G10S, although I was so nervous about losing the whole assembly that I used a strip of electrical tape to make sure it could not pop-out. For the record, this worked fine and the WiFi was flawless during the gig.
I did however make the decision to return the G10S. I honestly don't fault Line6 as this is clearly related to a non-standard jack on my bass and not a design flaw with the G10S. I just don't feel comfortable as-is and the music store I purchased at is willing to exchange the unit and allowing me to buy another system (from another company) that has the stomp box format, but utilises a transmitter that attaches to the strap as opposed to the input-jack design.
The one recommendation that I would share with Line6 is that you could have an FAQ page that lists common instruments that have reported this issue just to give buyers a chance to avoid the frustration. Sounds like there may be a few that exhibit this behaviour.
David.