Sadly, when the arborist came to deal with the tree with the spreading branches, he told me the silky oak tree was bifurcated (starting to split down the middle) and would soon become dangerous. A second silky oak was also becoming dangerous because the water board had cut through the roots near the trunk in order to access the sewer ( the tree was planted in a sewer easement, to they had the right, but I am a bit cross they didn't tell me what they had done). Both silky oaks were about 15 meters tall, so could cause a lot of damage if they fell over.
He also told me that one of the Alders was dead and needed to be removed.
So I suddenly went from 5 large trees along the back fence line to only 1 :(
And here is the pile of mulch that is all that remains of the silky oaks ):
I wanted to plant at least one new tree straight away, to make the garden a bit less barren. My parents, lovely people that they are, gave me a flowering gum sapling for Christmas, and Dad even came over and planted it for me! Given that this required digging out a quantity of heavy clay soil and filling the hole with bought in soil, this was a lot of work. The new tree is planted well inside the fence line, and should only grow to 5 meters, so it is unlikely to cause a repeat of the problem with the previous trees.
So I now have a new raised garden bed, with a flowering gum.
Here is a picture of the gum, and a picture of the first flower it put out for me:
I have a bit of work to do, putting in new plants to fill out the garden, but I want to take my time for the rest, and think about what I want.