I dont know crap about CFI except that the injectors are prone to leak.

And that should be easy to find out.

And do you try flooring it to start when starting hot?  The computer sees
that and shortens the injector pulse.

dig deeper into the electrical and you will find the problem.  

had the same problem on my LTD II.  got the recall notice and took it to
the dealer.  before then had the same problem you are having.  fire up
great when cold and would start right up if you didn't let it sit for
over 10 minutes.  after 10 minutes,  you would have to wait hours so the
engine would cool down.

well, the dealer said the replaced what the recall was for.  i picked
the car up and all that day, it started and ran fine.  next morning,
dead as a door nail.  would spin, no start.  like no spark.  called
dealer.  they sent tow truck.  when i went to pick up the car, they said
there was no charge.  when i asked why, they said there is TWO pieces
that make up this circuit and they replaced the one and not the other.
it was the other piece that they didn't replace that went bad.  no
problem after that for as long as i owned the car.

hope this information helps.

~ curtis

knowledge is power - growing old is mandatory - growing wise is optional    
"Many more men die with prostate cancer than of it. Growing old is
invariably fatal. Prostate cancer is only sometimes so."

For what it's worth, a couple pieces of advice from someone who has babied
an '85 LTD for the last 15 years:
1) You are saying 'or so it seems' about the presence of spark when the
engine refuses to start. Make sure to confirm that. Pull one of the wires,
attach a spare plug and put it on something metallic. Look for a spark while
an assistant works the ignition (or turn the switch to 'ON' and use a remote
starter). Works better in a dark garage. If no spark, I would look inside
the distributor. The plastic material which encapsulates the Hall effect
type pickup tends to disintegrate over time. Replacing the TFI might have
made it worse, because that's what the TFI plugs into. Check that the sensor
is intact and that the connection to the TFI is solid. The distributor needs
to come apart to replace the sensor, and it's not an easy thing to do. You
may be better off with a rebuilt distributor if you find that the sensor has
fallen apart.
2) Make sure that the fuel pump is working. You should hear it for a couple
seconds when you turn the ignition on.
3) Confirm that you have injector pulse. There is a $5 tester for this
purpose.
4) If no injector pulse or you can't hear the pump, check that the ECM
(engine computer) has power. It's powered through a relay that likes to
fail.
5) When the problem occurs, perform a KOEO diagnostic test. All you need is
a test light and a paper clip. Minor problems won't prevent it from
starting, but something major will. There may be a lose contact somewhere,
which disengages when things get hot and affects a lot. In my case, the +5V
reference would disappear, rendering every single sensor useless. If you
can't interpret the codes, post them here and someone will try to help you.
6) If you haven't found anything else, I would advise checking fuel
pressure. You can buy or rent the gauge. There is a test port on the fuel
line. Read the instructions and be careful not to spill any gasoline around
a hot engine! The TBI regulator is not vacuum compensated, so no rubber
diaphragm to break, but who knows.. You may have a bad pump, a clogged
filter, a grossly leaking injector - all leading to loss of pressure.
7) There is a simple instrument which will pulse the injectors and let you
check if they work properly by watching the fuel pressure.

Let us know what you found