Tree planting may achieve the same effect as a canal. If you make the interior greener as is postulated it was before man, then all you will be doing (by planting trees) is making the interior damper -> more flooding of Lake Eyre.
Now you are thinking. Nevertheless, some difficulties arise with this plan - not least that the trees you plant out in that part of the world will all die - it is
way too arid to support forest, or even woodland - although it certainly did in the past. (Not speculation this: there is any amount of fossil evidence demonstrating it conclusively.)
But the major part of the water that (sometimes) fills Lake Eyre doesn't fall anywhere near the place. Most of the water in Lake Eyre fell as rain in Queensland, many hundreds of kilometres to the north-north east. Camooweal, for example, is in the Lake Eyre Basin; so is Birdsville.
That is where you need to increase the rainfall.
And, you know, it's not by any means impractical. Most of that country has been cleared for grazing, and although it produces a lot of beef, the actual
profit from that beef is miniscule in the overall scheme of things. 90% of the profit made from farming in Australia comes from just 10% of the land - and you can be very confident indeed that not a single acre of that 10% is anywhere near the Cooper Basin. (Think places like Gippsland, King Island, New England, and the Atherton Tableland - that's where all the money is made.)
So you could revegatate vast areas of inland Queensland at remarkably low cost - indeed, by the time you factor in the various government subsidies and the actual long-term cost to the nation of non-sustainable farming practices, and the below-the-poverty-line real income of many outback farmers, and the substantial cost of community support services for poor agricultural districts (suicide help lines for just one example) .... factor all that in and you would probably find that allowing poor quality grazing land to regenerate would actually be
cheaper than doing nothing.
More problems need to be dealt with, however. Weed control would be a huge task, now that cattle have spread nasties like Horehound and Patterson's Curse and Capeweed and Onion Grass all over the continent (these are southern weeds - I'm not sure what the problem species up north are, but you can bet your last dollar that there will be plenty.
Transpiration rates will be a huge problem. Back when the continent was well-watered, a good deal of it was covered by old-fashioned rainforest-derived species (there are still pockets of this stuff to be found in northern Queensland - amaging stuff called "dry rainforest" - look it up). These plants transpired a lot of water through their leaves, and thus had a significant effect on the climate. But they were replaced by hard-leaved eucalyptus and acacia species which are water misers - these sclerophyllous plants can get by with less water than the soft-leaved older types (though the difference is much smaller than you might think) but more importatly, they can survive fire.
It is believed that fire was a key factor in the quite recent replacement of rainforest by sclerophyl forest in northern Australia - almost certainly, human activity was a major part of t.
Nevertheless, this is the sort of thinking which just might produce a worthwhile result. If you are going to dream, then start here - you have some faint hope of success, where the idiotic 1950's style of brute-force engineering schemes of the flood Lake Eyre variety have exactly zero chance of working as designed.