Solution? I think I've got one!
If we added a bit of roof from the bottom of the balcony, we could get the rain/snow/ice to end up in the garden where it would be of use - and save us breaking our necks and the house from suffering from the wet where it shouldn't be. We could rearrange two downspouts, too and redirect them to the garden. And while we're at it, we could add decking over the really old cement slab, and make a nice porch. A nice BIG porch - I measured and it would be 11'x35.5' - nice for a table and chairs and maybe a couple of rockers. I'd have to move some of the landscaping around, but not a huge bunch; just make a new path in front of the porch to go to the front gate.
So today I took a couple of pictures and worked out my plan in Photoshop. Just rough sketches, but they give the general idea:
As it is now (sure looks grim right now with the snow melting)
I think it looks good!
Side view as it is now
And how I'd like it
Next on the agenda is to get a few estimates. I wonder how much it would cost? I think Dean and I could handle putting in the planks on the deck and do the railing if we could get someone to frame the whole thing and put the roof extension (standing seam metal) on and redirect the downspouts.