I wonder if there’s a simple mechanical fix (apart from getting off your bike and walking it uphill)
Incidentally, there is one such fix. It’s called gears. I reckon (mostly based on personal experience, haven’t done any calculations), that even uphill, taking the weight of the bike into account, cycling is more efficient than walking at the same speed. (But probably not 3x more efficient, as it’s the case on level ground).
Biking is not always more efficient, as this quora answer points out: https://www.quora.com/Is-it-more-energy-efficient-to-walk-run-or-bike-up-a-hill/answer/Raj-Kumar-855
Regarding muscles, as an (former) cycling enthusiast, cycling uses a lot fewer muscles than running. The muscles used for cycling are some of the strongest in the body (hamstring, quadriceps). Compared to running which uses almost the whole body, including core muscles for stability, this is a downside for cycling, because it may not be as natural as running. But I wouldn’t say you end up tiring weaker muscles.
2. The speed at which balancing becomes effortless is roughly walking speed. It is actually difficult to ride that slowly (depending on the bike, load, windspeed etc).