Hi,
I have australian licenses so I understand what you are looking for with ICUS time.
There are hundreds of companies who offer the sort of time building you are looking for in the USA. Everything from Piper Seminoles to Gulfstreams.
A lot of companies like Ameriflight, ALpine AIr, Mesa, etc.. have programs where you can pay them to be the first officer on a 2 pilot crew for 6-12 months to build time. However, if you are coming into the country these days to receive flight training you want to be very careful to check the immigration requirements to receive any kind of flight training. Especially on larger aircraft.
I would recommend getting in touch with the FAA in Oklahoma City as a first stop.
The programs I have seen range from the $5000 mark upwards for a full time training program, lots of night, IFR flying.
If you have any particular companies in mind email me privately and I'll let you know what I know.
Weasil.