You can't get a service using Sprint/Verizon unless you actually buy a handset from them though. They are legacy CDMA carriers, and as such, they don't just 'sell SIM's' to people You have to 'activate' a Verizon device. GSM/UMTS providers do not roam with them either.
There are actually two A1429 iPhones, a GSM and a CDMA one.
I believe the actual bands that Verizon and Sprint used are only available on the CDMA A1429, and not the GSM models.
Try closer to 2G speeds on 4G or 3G on AT&T. It's nowhere near as good as Telstra's 3G speeds.
This just means you get better 3G coverage. 4G = LTE in most the world, in the USA they market HSPDA plus as 4G and 4G as LTE.
This is why you see 4G on your Australian phone running on an LTE network here, and 4G on an HSDPA network in the USA (if you look at the US based phones they'll say LTE). It's misleading, and you can blame AT&T for that one; they convinced Apple to do this on their handsets. Pre iOS 7, iPhones here in Australia said LTE for 4G, now they say 4G. Go to the USA with same phone? Says 4G.