I've always had a fondness for SOX lamps...It's good to know that SOX will have a future in private, even if its public brethren are being persecuted to the point of extinction.
Short of going completely original and re-equipping this old lantern for gas, I think SOX would be a good choice and be quite novel too. It would see off the existing CFL for good!
Obviously, the inclusion of this lamp will alter the daytime appearance of the lantern - it might look good...or it might not.
The only other things to bear in mind is that an unshaded 35W lamp can be uncomfortably glaring at night, especially when at the relatively low mounting height likely to be encountered here (your neighbours might not be so enthusiastic either). The monochromatic radiation at 589nm is closest to the human eye's peak responsiveness, hence its great efficacy - but I'm sure you'll know that already!
In addition, as the lamp would typically be burned "cap up", most of the light would be thrown out sideways, with only a small amount reaching below. An alternative solution would be to mount the lamp on the horizontal via a special reflector, mounted in the "eaves" of the lantern. This will stop any upward light being lost "to the moon!"
The slight problem here though might be a lack of available space in which to fit the lamp - we wouldn't want to recreate a version of the Rochdale seagulls! Should this be the case, a better prospect would be an 18W SOX-E. With a simple trapezoidal shaped reflector made of opal perspex fixed to top end, the lamp would fit in, the light would be reflected downwards, plus you'll get that characteristic glow through the opal lantern top - very nice!
The gear could be mounted remotely as you suggest, however it may be possible to mount it internally above the reflector, thus reducing wiring. If I can, I'll pop a few drawings in to better explain this idea.
I have done a similar sort of thing with my garden lamp. It is a cut down cast iron column with swan neck. Total height to its Z9480 lantern is only about 8'. As I wanted it to remain SOX but mindful of upsetting the neighbours, I repositioned the lampholder bracket so an 18W lamp could be used and would still be central. The gear was from a scrap Philips bulkhead. Powering the lamp up was rewarding but also introduced a slight problem. The light was still too bright for the area, therefore it needed to be toned down. A handy tip is to use expandable plastic cable braiding. It is available in many sizes and is easy to cut and fit. When slid over the lamp, the light still gets out but is slightly reduced in brightness, as some of it is blocked by the braiding weave. Due to the relatively low temp the lamp reaches, there is no risk of the plastic melting. Light output is now more "in scale" with the mounting height and has run with no problems for many months now.
Anyway, it's a thought.