A few more things to check. Heater core for leakage, check carpet under heater for moisture. Radiator overflow tank, these are known to crack.
Does the oil looks OK, not a whipped texture, brown in color. The white smoke smells like steam?
Here are a few things to try. Some might not be practical for you.
Let the car sit overnight. Pull the plugs and place paper towels over each cylinder hole. Make sure you mark each towel so you know what cylinder it was covering. Then turn the engine over. Any water in the cylinder will be blown out and into the towel for you to find.
Or better yet pressurize the coolant system to 20psi and wait a couple of hours. A shop can do this or pressure pumps are available at auto stores. Then do the paper towel test.
Engine cold, radiator cap off. Fill the radiator with coolant to the brim. Start the engine and race it. See if the coolant is pushed back out of the radiator. If a blown gasket or cracked head, the exhaust gases may force the water out. Some times this can be very violent. Be careful, as coolant is toxic and attractive to animals and small kids.
Take a look at the spark plugs. Does one or more (usually adjacent cylinders) look different? Perhaps cleaner, as in steam cleaned? You might try this shortly after you have run the engine a minute after a cold start up. See if one or more plugs have water on it. The water that is coming out the exhaust pipe.
A compression test may reveal a low cylinder(s), again usually adjacent to each other.
I have heard you can take a sample of the coolant fluid to a radiator shop or auto repair place and if set up, they can test it for hydrocarbons. A sign the exhaust gas is in the coolant.
The idea is to know with a great deal of confidence if it is a heat gasket or cracked cylinder problem. Most likely you will not be able to determine which. Unless the motor was overheated, it is most likely a head gasket.
Did you ever overheat the engine or run out of water?
A good shop should be able to run down this problem, it is common on cars in general.
1000AU is about 730US. Can you have someone repair at this cost? If only the heat gasket, yes. But it depends on the shop hourly rate. Toyota lists a repair time of 7.5 hrs plus $65 for a gasket. An independent shop may have a much cheaper hourly rate. Removing and replacing a head gasket is not complicated, it does take time.
Some concerns. If the head is cracked this will add to the expense. It may be able to be welded, but you will not know until you have it inspected. Often a mechanic can tell from looking at the removed gasket if it is just a gasket problem. Sometimes a good used head can be found. The head can be OK but warped. This is common and would require resurfacing the head. This is not a big deal but is another cost. Often car owners also have the valves reground but this adds to the cost.
Check around for estimates. This problem is again common for cars in general. A decent shop can provide a good estimate and explain all the issues. A good home mechanic can also do this repair easily. The head can be sent to a shop if it needs resurfacing or repair. Perhaps you know someone who works on cars.
90K is not that many miles for a 5SFE. As such I would defer first to the warranty. A blown head gasket or cracked head on this engine is not normal wear and tear. The cost of repair can add up depending on what is found after disassembly.
Post back with what you have found out.