Pachyderm - welcome to the forum. You mentioned that since you got the saddle "sorted", now your shoulders and back hurt. Perhaps you need to check out the fore/aft position - it could be that you're too stretched out or too bunched up which could cause pain in the shoulders/back. Saddle adjustments are a nightmare, but once it's right, you almost want to super-glue the thing in place! It sounds like your puppy-sitting will help your fitness, even though you won't have as much time to concentrate on your biking. Try making sure you're pulling your abs in when you walk. I often get backache when walking - pulling in my abs and pulling up/straightening my shoulders takes the pressure off the lower back and really does help (I have terrible posture!). This could also help on the bike - let your abs take the pressure, not your shoulders/back.

I was about to ramble on about body fat scales, but Natheless beat me to it!
It's impossible to compare readings taken from different methods - or even different scales. My body fat scales would vary quite considerably if I'd had a cup of tea or even a pee beforehand! I second the advice that the only real way to measure fat percentage loss is to use the same method, under the same conditions and stick with that when making comparisions.
Body fat percentage (when accurately monitored) is an excellent way of checking your progress, it gives slower results that weight scales, but is more indicative of how things are going.

In terms of better machine giving a better quality workout - again, I'll echo what's already been said and say it depends on what kind of workout you're aiming for.
My lightweight road bike is a joy to use and keeps me on the bike for longer, both time and distance. My road bike has helped me master hills and made me faster on the flats.
I commute on a clunky old hybrid, which weights practically as much as I do! I once commuted on my road bike and flew there and back - eating up the hills and flying on the flats. But my hybrid is a workout in itself - I chug up the hills, nice fast spin, steady heart rate - I don't go anywhere fast on this thing but it does give me a different type of workout. I hate it with a passion and would never take it on a weekend ride, but it's my trusty old friend and helps me concentrate on being slower and steady, and think about form.