There's a lot going on here.
It sounds like you have the basic setup correct: power point -> step-down -> timer -> power supply -> enlarger
If the enlarger worked properly with the 12V Australian supply, then you likely have a 100W 12V lamp. Hooking it up to the 82V american supply will kill the lamp quick, although you should check all the fuses in case you got lucky.
If you want to continue with the 110V setup, all you need to do is swap in an 85W 82V lamp. KHB are a good source, just specify air mail (Canadian surface mail takes months to arrive). Make sure you get spares
If you want to swap to 240V, you drop the step-down transformer, add a 240V timer, swap the 82V supply for a 12V supply (get a 12V AC supply - no delay in turning the enlarger off), and go with 100W 12V lamps. 12V AC supplies are fairly common - they're used for garden halogen lights. Get one in the 120-150VA range. You'll likely need to do some wiring on the 12V side - never touch the 240V side and only work with everything unplugged (12V is fairly safe, but better safe than sorry). It would be wise to add a fuse holder and 10A fuse in one of the leads if the supply doesn't have one.
By the way, the 500W step-down is overkill - if you can return it, swap it for a 120-150VA step-down.
If you have any questions or if anything is unclear, let me know.