"the fact is that with training you absolutely can change the ratio of fast to slow twitch or vice versa"
This implies growing muscle fibers, not enlarging them. This also implies that you could take a marathon runner and turn him into a ranked powerlifter. Individuals are born with a certain number and type / mix of muscle fibers. One can can train either fibre but there are those with body types more conducive to a specific type of training. Can you please provide a source of this ability to change the ratio?
"If you lift for increased power production, you will not improve endurance"
Power and strength are NOT the same things. Training for power involves using light weights and moving them very fast. Indeed, it does not improve endurance. But we are talking about strength training.
"slow twitch are what we use to hike"
No, you cannot will only the slow twitch muscles of your legs to contract. Muscle fibers contract as an 'all or nothing proposition.'
"Look at the different builds of cyclists in the Tour de France: the climbers are all lithe and skinny...that is endurance training"
Much of that has to do with diet and the fact that they are burning so many calories. And the fact that they have to remain light to go faster and farther. Their upper bodies are skinny but the legs on some of them are hardly small. Quite enormous, in fact. Size and strength are not necessarily correlated because diet becomes the equalizer (there are 180 lbs men who are 5'8" and squatting well over 600lbs). And of course, many of the cyclists of the Tour de France DO strength train - heavy squats, and their performance has improved measurably.
"To really improve a muscle's force production you actually need to lift enough weight to be tired after 8-10 reps...and to not be able to actually finish that last one. Then do another set. This kind of training will do nothing for endurance."
First of all, strength training does not require training to failure / fatigue. In fact, it is really counterproductive for strength because it prevents sufficient volume at heavier weights and can negatively affect your Central Nervous System during the supercompensation phase (see Nikolai Jakowlew). You need to train at a level that is above a specific percentage of your one repetition maximum but this does not mean fatiguing the muscle until it can't contract. Can you imagine hiking that way? Hiking until you pass out due to fatigue?
Say you can lift 100 lbs for 10 reps and 25 lbs for 30 reps today. If you can lift 200 lbs for 10 reps in 6 months, how much weight do you think you could lift for 30 reps. More than 25 lbs? Sure. Lets say 50 lbs. Now if you were to lift 25 lbs again, I can guarantee that you will lift it for many more reps than 30. Guess what just happened. Your capacity for work has increased and thus your endurance. To put it another way, a stronger muscle does not work as hard as a weaker muscle to produce the same force, providing a lot of stored energy in reserve should it be required. Strength training simply improves the muscle's ability and capacity to do more work.
Looked at it another way, the endurance of the muscle increases because at any level apart from a maximum effort defined by a failure of the muscle to contract, a stronger muscle can contract FEWER muscle fibers without failing than a weaker muscle and hence, it will have a higher level of endurance.
Chilibeck PD, Syrotuik DG, Bell GJ. The effect of concurrent endurance and strength training on quantitative estimates of subsarcolemmal and intermyofibrillar mitochondria. Int J Sports Med. 2002 Jan;23(1):33-9
Hickson RC, Rosenkoetter MA, Brown MM. Strength training effects on aerobic power and short-term endurance. Med Sci Sports Exerc. 1980;12(5):336-9
Hickson RC, Dvorak BA, Gorostiaga EM, Kurowski TT, Foster C. Potential for strength and endurance training to amplify endurance performance. J Appl Physiol. 1988 Nov;65(5):2285-90
Marcinik EJ, Potts J, Schlabach G, Will S, Dawson P, Hurley BF. Effects of strength training on lactate threshold and endurance performance. Med Sci Sports Exerc. 1991 Jun;23(6):739-43
Bastiaans JJ, van Diemen AB, Veneberg T, Jeukendrup AE. The effects of replacing a portion of endurance training by explosive strength training on performance in trained cyclists. Eur J Appl Physiol. 2001 Nov;86(1):79-84
Paavolainen L, Hakkinen K, Hamalainen I, Nummela A, Rusko H. Explosive-strength training improves 5-km running time by improving running economy and muscle power. J Appl Physiol. 1999 May;86(5):1527-33
But no question the biggest supporter of this thought is experience. Piper has proven to all of us that specific strength training results in working far less on the trail, with fewer aches and pains, and with increased 'gas in the tank.' Considering she has thru-hiked, I am most impressed that she has generated far superior results from strength training that sport specific endurance training.
Edit: Tom, is this incisive enough for you? Ha!