To paraphrase the old sci-fi warning, there is nothing wrong with your body (rather than "there is nothing wrong with your set..."). It's just getting old. Not being able to have a lift, crawling under the car is unavoidable. Getting down isn't so bad but getting up can sometimes be a challenge. Then there are the times when you need to get up and down lots of times (to get a different wrench, the unexpected tool that was needed, etc...). I think it helps to think about that in terms of doing an exercise. And just like exercise, you will be reminded of all you did today, tomorrow! It's hell getting old!
As for taking the motor out with the tranny, I suppose that would be ok but remember getting the motor out from under the car will require the car to be pretty high! For me, I think I would tend to opt for taking them both out from the top. I've taking the tranny in and out several times - always out the top. I've not had to take the motor out yet (thankfully!!) but my first thought would be to pull it out from the top too but I suppose a lot depends on your situation and what you're comfortable (nice word to say when we're talking about getting up and down at our age!) doing.