I don't think you can stretch the ring into a cylinder shape. They seem to have gained great functionality by making the ring a "rounded donut" shape. Stretching it would probably return it to requiring 'planet Jupiter mass' energy requirements. I would think that multiple donut rings in series would also.
I think best to just use the saucer-section. Scaled to the max diameter of the football (in proportion to the warp ring), and mount it on a pivot axis to the ring. Then, with the saucer perpendicular to the ring... it's impulse engines can be used to achieve initial sub-light velocity. Then pivot the saucer to parallel with the ring, and engage the warp drive. When slowing to stop... do the reverse procedure.
A. Why pivot it at all?
B. Why use a saucer shape to begin with?
Sorry - my bad. I was thinking of two size-scale ships at the same time. I'll try again.
If the Enterprise saucer-section was no larger than the 'football' ship... then no pivot is needed. But if the saucer is scaled larger then the 'football' ship... then pivot is needed to prevent the saucer's leading and trailing portions from extending into, and being destroyed, in the 'close' warp zones ahead and behind the warp-ring.
The 'saucer shape' is what the Enterprise uses as it's primary hull shape. And it might be desired/required to disconnect from the warp-ring, and land the ship (proper) on a planet. Perhaps as a colony base station.