Just finished this project. Did starboard last winter and portside this week. Both while balancing in the dinghy, which isn't really any worse than balancing on a ladder, and safer!
After removing the stainless steel strip from the teak rubrail (below the teak caprail, which remained untouched during this undertaking), the screws holding the teak rubrail itself are revealed. These are ridiculously long and screwed deep into the hull. A few of them broke off from sheer torque during removal, most were extracted and two were cut by shoving the blade of an oscillating multitool under the rail from the bottom upwards. The rest came out fine and were re-used. It's fine to replace the broken ones with somewhat shorter ones, as long as they go at least about 1cm into the fibreglass - no need to use super long ones, which are hard to find.
On ours, the teak was installed while the sealant on the deck/hull joint was still wet, so excess sealant stuck on the teak, making it difficult to remove, but after some prying it all came off without significant damage to anything.
This reveals the rather atrocious job the factory workers have done in 2000/2001 when our boat was built. There are two thick sausages of sealant in the joint, but no attempt was made in smoothing anything and adhesion was extremely poor in most places. No wonder it leaked! A few areas adhered well, but elsewhere you could pull on the sealant and a 0.5 to 1m long section would just come out with no resistance. Perhaps they didn't clean or degrease the parts first?
I removed most of the outer caulking "sausage" wherever it was loose, which was most of it. Left the second one, deeper inside, in place. Then cleaned up everything with soapy water and a stiff brush right into the joint and let it dry over night. Wiped it down with acetone the next day and then started caulking. There's a lot of space in there and surprising amounts of caulking go in - three cartridges per side, six in total. I used a modern MS Polymer sealant for durability, costs around €12 a tube here (white - not that it matters). I cut the nozzle to a medium size and shoved it into the joint (which varies in thickness quite a lot) and got the sealant right into there, with a little squeeze-out that I then smoothed over with a finger, covering all the exposed fibreglass to make a clean and waterproof seam.
After letting that cure over night, the rubrail went back on. On the starboard side I sanded and varnished it, but sadly it turned out on the portside there isn't really enough left of the teak, too much has weathered away and sanding it would mean it wouldn't be wide enough to carry the stainless strip anymore. So I just put the stainless strip back on for now. Might replace it with PVC eventually. There's also some gaps between the 2m long pieces to connect with black sealant, although this can be done later.
The job took me 3 days per side, although I hurried a bit as we're at risk of losing access from the dinghy (marina might put a boat in that berth).
Bit dry without pictures, might dig up last year's later. Didn't get any this time due to hurrying!