An excellent substitute for barbell squats is exactly what you're doing: dumbbell deadlifts. You want to have the dumbbells almost touch the floor at the bottom and your body to be totally upright at the top. Try to bend over as little as possible, which will still be a lot, doing as much as possible with your legs. Moving relatively quickly is good, partly because the dumbbells are hard to hold on to. This is a fantastic exercise for the whole body. One of the tests for being over the hill is grip strength, so this'll take care of that, too. Right now, I'm doing 3 sets of 10 with 50# dumbbells. When I was in shape, I remember using 60#.

Depends on one's definition of overdoing it. Lifting more weight than one is ready for and getting injured is definitely overdoing it. Getting so tired at the gym that you'd like to have a wheelbarrow take you to your car is what one is after. It's not lifting more weight that one is after, really. Simply getting tired is the goal, not that different from a hard hilly ride. I used to say that if one could still walk at the end of the Sunday ride, one could have gone harder. So it's the same thing, just with more force and way fewer reps than one does on the bike. The goal is simply greater force production. The more force one can produce, the less one tires at a lower force production. One is then loading each of the available muscle fibers more lightly on the bike. One way to look at it anyway.

Think of what you're doing as simply riding really, really hard out of the saddle.