Bloody Blue Gum

I fight a losing battle with these messy trees; the blue gum is the worst and trying to develop a nice verge is near on impossible. I need help. I would love to have a bit of a flower bed against the wall with small grevilleas or hakea pin cushions to attract more birds. A lawn would also be nice. I have a bore so can provide the water but the mess from the trees makes it very hard. The council has had it trimmed but maybe not enough.

I am on a corner block and need help all round really. I have just painted the gate and panels to improve the look. Guidance appreciated.