I will try and give you a few new suggestions to give you more homework. I have been having intermittent difficulties with my 94 T100 3.0L V6 for some time now and having poured over many repair manuals, specs, and websites looking for the culprit I think I may be able to help you look for the problem in different areas you may or may not have looked at just yet.
It doesn't seem that you have any problem with the fuel pressure, but I find your testing rather interesting. I have the specs for the pressures in the different states here somewhere for the 3.0L V6. I have some other links that I will add if I can find them as I am typing this.
I think the first thing I would try is to pull the EFI fuse (Possibly different for your vehicle) under the hood for 15 seconds to reset the ECU (you will lose all codes stored in there so check it first). Then just see if it starts. It could be the coolant temperature sensor, the oil temperature sender sending or not sending proper information.
Toyota's in general do not like poor grounds. There are an unlimited number of possible problems that can be related to poor grounding somewhere on the vehicle. I recommend going below and reading about the Automatic Downloading of Toyota Service Manuals to get your hands on the wiring schematics and starting ciruit for your vehicle. Find all the harness and engine grounding points and make sure they are intact.
Ignition switches can cause a number of problems if they are worn out by giving varying amounts of voltage at different times. Possibly not allowing all the systems to function properly. This can be hard to diagnose. One way to evaluate the general charging system voltage is to buy a digital charging system monitor that plugs into the cigarette lighter and shows voltage on ACC / On and after starting as the vehicle is running. You can add more systems to see if you are getting unusual spikes or draws anywhere or if you are getting different readings on different drives. This is only a basic guage of the charging system. Before the first starting the a good battery is 12 V to 12.9 V. During Charging it should be 13.5 V to 14.5 V. You should see feel an increase in idle speed when the A/C is on and the voltage drops at a stop light. If it does not then there could be a problem in the charging system, sensor, or ECU. You can buy the tester for $15 at Walmart or Autozone. One way to clearly see if the ignition switch is the problem is to install a bump switch or remote starter to completely bypass the ignition system. Just put the key in the on position and push the button on the bump switch and the starter should kick in with full battery voltage. These run about $15 at most parts stores or Sears.
If you disconnect your Circuit Opening Relay (near ECU on my vehicle) then remove your gas cap and then turn over the engine you will depressurize the fuel lines. If you can't get to or find the Circuit Opening Relay then you can just disconnect the wiring directly to the Fuel Pump, but you will have to go fishing under the vehicle to do that. Just reconnect the relay and gas cap and if pressure was your problem then it should start during or after this process.
The first thing that struck me as I was reading your problem was that you have been spraying starter fluid into the throttlebody. The Throttle Possition Sensor is very sensitive and can be ruined by this. If you remove the hose to the Throttle Body you can see a small hole near the bottom. That is where the Throttle Position Sensor gets its readings. Starter or Carb cleaner in that hole can damage the sensor. Done often enough, can also ruin the O2 sensors. Which would, assuming the ECU is working properly, not allow the ECU to properly judge exactly the proper amount of fuel to send to the injector (including your cold start injector which should normally get extra fuel at each startup unless it is clogged or not functioning). The cold start injector is easy enough to check resistance following the repair manual. Check out the link below for more information on Throttle Position Sensor.
A long shot considering you replaced the coil is a weak spark or improper timing. You can get an inline spark tester for under $10 at Autozone or the like. It has a light that flashes with each spark and you just move it from spark plug to spark plug between starts. My Toyota has to have the DLC1 jumped in order to properly adjust the timing. Also the ECU is taking a reading of several other sensors as the vehicle is starting and while it is running adjusting the Fuel/Air ratio and spark timing for each cylinder. Other sensors to check could be Knock Sensor and Crank Position Sensor.
A poor or bad connection with the starter solenoid (intermittent clicking while trying to start) can cause reverse polarity or arcing potentially sending excessive power to sensors, relays, or the ECU. The likely problems in this circuit are the Circuit Opening Relay, the Fuel Pump Relay, Starter Relay, ECU, and EFI fuse, IGN fuse. There are several other items that could be affected, but these are the front runners. I would consider the ECU as one of the most likely suspects. Considering the expense of replacing this unit, if at all possible, borrow one from someone with the same vehicle just to test the possibility of this being the culprit. Testing the ECU is very difficult and time consuming. Your vehicle can drive mostly fine with a bad ECU under many circumstances. The one thing that seems very strange is that you don't seem to mention any Malfunction Indicator Light coming on or any codes from the ECU. Check out the link for the Solenoid Saver Diode below (under start links).
The best thread I found that may help you out is one from NaterGator for an automatic download of Toyota Service Manuals. You can get all of the manuals on your computer and get all the specs you could ever wish for. The link is below under Manuals and Training.
Another long shot could be vapor lock. I haven't heard of it in these vehicles and would be unlikely in pressurized systems. That could explain the time needed to cool down. Is there any possibility that any fuel line or intake manifold could be close enough to a heat source to get hot enough for this to happen? See links under Fuel System for detailed information on injector system and complete testing.
ECU Diagnosis and Repair links:
http://www.enginecontrolunits.com/index.html
http://www.autocomputersupply.com/index.asp?PageAction=Custom&ID=5
Starter Soleniod Diagnosis and Repair Links:
http://www.4crawler.com/4x4/CheapTricks/Starter.shtml
http://www.sherco-auto.com/contacts.htm
http://www.fostertruck.com/sol-saverdiode.htm
http://www.fostertruck.com/dodge/starter faq.htm
Throttle Position Sensor diagnosis and repair links:
http://www.4crawler.com/4x4/CheapTricks/TPS/index.shtml
Service Manuals and Training:
https://forum.ih8mud.com/showthread.php?t=128021
http://www.techinfo.toyota.com
http://www.autoshop101.com/
Fuel Systems links:
http://www.autoshop101.com/forms/h22.pdf
Let me know if you trace the problem or have any questions I may or may not be able to answer. Good Luck!!! Paul
pwc@cox.net
In this case it was the fuel pump...great info and thanks for posting the links. 
