Warm up injector...stuck?
 

Is it possible for the warm-up injector to become stuck open or leak enough fuel to cause a hesitation on acceleration from idle?

Slightly possible, but not likely. This sounds more like a too lean air-fuel mixture. You'll need to bite the bullet and get the fuel presure gauge setup with the in line valve to find out what's going on. Trying to troubleshoot K-Jet without the gauge is like troubleshooting a modern fuel injection system without a scan tool and DMM; possible but difficult, and can lead you to replace good parts.

Now, it is possible to adjust the air-fuel mixture adjustment to give a good idle (assuming all else is OK), but if the control pressure is too far off, you'll just end up with a lack of top-end power because the air meter can't open up the valves in the fuel distributor far enough to let in the correct amount of fuel against the too-high control pressure.

A leaking cold start injector is more likely to cause starting problems due to fuel bleeding out of the system with the engine off.

My advice is to beg, borrow, or buy the gauge then report back with your findings.

Ok, that raises my suspicions about vacuum leaks..I know I have some.

Spray carb cleaner around areas of suspected leaks. A surge in idle will tell you you've found one.

Where can I get or how can I make such a gauge?

Here's a ready-made gauge:

http://www.etoolcart.com/cisk-jetfuelinjectortesterta33865.aspx

Or, you could make one up with a 100PSI gauge, an in-line valve, the proper fittings, and about 2' of rubber hose. The in-line hose assembly with the valve will take the place of the line that goes from the fuel distributor to the warm up regulator. You will need the matching fittings on your hose assembly. The gauge will connect to the fuel distributor side of the in-line valve.

What you're looking for is the proper pressures, which depend on the engine temperature. Closing the test valve with the car running will give you the system pressure, which should be around 5.5 bar (550kPa). This pressure being too far off can cause problems with control pressure. Opening the test valve will give you the control pressure. This will vary with engine temperature. Lower control pressure gives a richer mixture, and higher pressure leans it out. I don't recall what the cold control pressure should be (it's in a chart in the shop manual). The normal operating temperature control pressure, IIRC, should be between 3.2-3.6 bar (320-360kPa). This is critical for proper engine performance. A too-high control pressure can give you the hesitation symptoms you have. It can be caused by debris in the WUR. If you do these tests, at the very least you'll be able to rule out the fuel system as a cause, and if not, get a better handle on what's wrong.

Keep in mind that it is possible to adjust the air-fuel mixture at the air flow meter for a good idle with incorrect control pressure, but then the performance of the car at speed will be wrong. The movement of the sensor plate is balanced by the control pressure at the top of the plunger in the fuel distributor. Too much pressure will not allow the sensor plate to move as far as it should with the result that not enough fuel can be metered by the plunger. That was done to my car as I found out when it had a serious lack of power at speed. The control pressure was about 5 bar, not 3.6 bar like specified. It turned out to be a clogged filter screen in the WUR.