If most women over 50 have it, it can't be due to ice dance boots...
>>I was taught to lean forwards when skating forwards, and back when skating
>>back, to the amount needed so the weight is centered.
>So was I. That's why I am wondering whether on short blades when skating backward,
>when I put my weight back I will fall backwards on my bottom.
If you always center your weight on the blade, you won't be on the part of the blade that would cause you to fall backwards. But if you sometimes center your weight behind the place the tail ends on Dance boots (say, on back 3-turns or counters, or back twizzles), and you feel you can't adapt to the change, you could fall. Maybe you could have someone watch while you skate backwards and do back turns, to see how far back you normally roll.
For whatever reasons, ice dancers place usually more importance on "neat feet" than freestyle skaters, which means the feet should often be close to each other. Having shorter tails makes that easier. That said, many ice dancers do use freestyle blades, yet do well.
But if you are switching from freestyle to dance boots, maybe it makes sense to keep your old blades if they are still OK, and see how they do? Maybe it is easier to change one thing at a time.
But it's your choice. We can't decide for you.