How stay fit enough to make moderately hard rides a couple times a month? When I have time I like to get my bike and canoe out and do a day trip.  Doing a mile or two is not hard but a good day trip is between 8 and 14 miles. When I started at the beginning of the year 6 miles was all I could do before leg muscle fatigue (and butt soreness) did me in.  Now at the end of the season I can just make 14 miles in 3 hours with a bit of walking the last few miles.  I did a 22 mile bike only trip last week with similar results near the end of it.  So I am guessing 1 bike/canoe mile =~ 1.5 or 2 bike only miles.  

I usually bike/walk straight through as going down the river is much slower (2 or 3 mph) and getting to the planned boat ramp before dark is critical. The trails are mostly rail to trail and unpaved. Friction, wind resistance and towing an extra 100+ pounds up a gentle slope, are the major impediments. I find a casual pedal of about 5 or 6 miles an hour to be the most effective. 

My scheduled exercise time is an hour, 3 mornings per week.  Which include free weights, elliptical and recumbent stationary bike (wife's choice for our home gym). I found several related questions they all pretty much say to ride about 2/3 of your hard ride a few times a week.  I am looking for a solution that will allow me to do a really hard 20 minute exercise that equate to a 2 or 3 hour casual pedal.  

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The difficulty is you want specifically to train for endurance, but you want to do it in short bursts.  

I'm not saying a few squats won't help a bit, but they won't do the job.  And trying to push too hard on a bike for a few tens of minutes might improve your aerobic capacity but quite possibly at the expense of your knees.  You also need to be in a similar geometry so the benefit of an hour or 2 of moderate pedalling on the recumbent while reading/watching TV will be limited.  However (almost) within your constraints that might be the best place to start.  Or drop the elliptical in favour of more bike time if you really don't want to increase your total time.

That's the fitness aspect; the soreness will only be dealt with by time in that saddle, or one very similar.  If the saddle suits you you don't need ages in it to keep yourself at a level suitable for spending 3 hours on it, but you do need to get on it every few days at least.

Anything you only do a couple of times a month will be hard, skipping anything over a week or two really hits your fitnesss for a specific task (a shorter figure even than that is often quoted, but in the context of an athlete's peak performance rather than something more casual).

I'd also suggest that particularly as you build up the long towing rides rather than walking at the end you take a decent break and ride again.  This will be tricky if there are uphills involved, in that case you might get away with a walk or 2 earlier in the trip.

One further suggestion given comments and other answers: switch one of your mixed exercise sessions per week to bike only from a month before your first ride/paddle trip to a week before your last of the season.