I just measured my gin pole (26S - slightly shorter mast than the 26M) and with the connection bracket, its about 6 foot 3 inch. I have been using a beefy quick connect on it for years.
If you do that often, I think a jib furler would just be a huge pain to deal with plus more likely to damage something in the process of raising and lowering so you might be better sticking to hank on jib. You may also need some sort of custom mast crutch. A longer mast crutch holds the end of the mast higher making it easier to raise the mast but it also would result in the end of the mast being too high for your clearance. You would sort of want a very low crutch to go under the bridge but a high crutch for raising and lowering the mast.. And its possible that with a stern rail, you just cant get the end of the mast low enough without also disconnecting the base of the mast and bring it forward like you would do for trailering..
And.. another "problem". If you have a fairly high mast crutch, you can simply disconnect the boom from the mast and leave the main pretty much all set up when the mast is lowered. Makes for a quick re-connect after the bridge. However, this has limits on how for down the mast can come. If you need to really bring the mast "way" down, you may have to also remove the main sail slugs.. etc. Sounds like a hassle.. but you probably could make it work.