Since then I have rebuilt the carb and adjusted the curb idle screw, idle mixture screws and the accelerator pump bolt to the specs I've found on the internet or from Holley.  Even purchased a vacuum gauge to make sure I'm doing it right.  The highest reading I could get was about 16 in Hg.  The vacuum gage shows that right on the line between normal (green) and late ign. timing (red).  So I thought I'll check the timing and it was right on 10 deg. BTDC.  I tried advancing and retarding the timing a couple of degrees each way and it made no difference.  I also put new spark plugs in as the ones I put in at the beginning of the season looked carbon fouled.  Finally I did a resistance test on the ignition coil and spark plug wires and everything seemed good according to my research.  

So I have spark, possibly too much fuel, and maybe to little air? 

Please help me diagnose this issue as I am afraid I might be making things worse just letting it go.   

A few things come to mind.

I know you inspected your distributor and found the paper, but not sure you ever took a look at your advance mechanism to make sure springs are ok (as suggested above) and it's operating correctly.  When running, does it run up to WOT with no hesitation?  Feels like it has the power it should?  Not sure what you have for a timing light but one with advance would tell you more about how it's running.

Did you inspect the fuel line and anti-siphon valve at the tank?  It would be good to get a fuel pressure gauge and see if you have adequate fuel pressure when cranking and running.

Just crack the throttle a little a leave it there till it fires to clear it out.

Vacuum seems a bit low. that needs to be investigated.

Also set idle mix for max vacuum under load in forward gear, else if done at neutral it will be weak in gear,  hard to restart after a quick shutdown, the delta-rpm between neutral and forward will be frustratingly high, anad will not launch hard and sometimes stall when you punch it.

The starting when releasing the key needs to be addressed.  Cables and connections cleaned

for diagnosis, unplug the choke for a restart, that will raise the energy available to the ignition.

if improved,  there is too much voltage drop on the old wires.

Also, what sort of battery is in the boat?

Travis Eacret wrote:   Another unusual thing is it seems to catch most of the time right as I am releasing the key.

Is there any way it could be mis-wiried such that there is no power to coil while cranking, but power when key is at on position?

So thinking this was an electrical problem I started testing voltage from the battery and following the cables on up to the helm; I didn't find any significant voltage drop (over 10%) until I got to the 3 way ignition switch and I was losing like 50% of the voltage.  Starter was ok, solenoid was ok, and unplugged any connections I found prior to the helm.  Checked impedance on the ignition switch on the dash and the 3 way ignition switch and they seemed ok.  I looked at most of the electrical connections under the instrument panel and nothing seemed loose however I still unplugged quite a few and plugged them back in including the horn which previously would only work if the motor was running.  There must have been something causing voltage drop under the instrument panel because today I put things back together and had over about 12.6 volts on the 3 way ignition.  I tested the engine in the drive running in neutral and it started right away cold just needing a few extra RPM's to get warmed up, and also started instantly after warmed up with no pumping of the throttle and it didn't matter if I let it sit a few minutes or not.  I also found a place to connect the vacuum gauge directly to the manifold and was able to get a reading of about 18 Hg at just under 700 RPM's.  I also verified the timing was still at 10 deg BTDC.  

I understand that I should make adjustments in gear under load but I could not do that today and I just took the opportunity to winterize the boat while I had it out since the forecast calls for multiple nights below freezing.  

I know I wrote a book but typing out my problems and thinking through the symptoms a little slower along with suggestions from the forum helped my get my boat running.  

Thanks and Happy Holidays

Good job. Even though you didn't find the exact problem spot, glad you were able to correct the hard start. Bad connections typically due to corrosion in the moist marine environment are pretty commen. Besides connections, contacts inside switches can also cause problem. If the problem comes up again, I'd suggest going back to the connections cleaning them and then use some dielectric grease when reassembling. I'd also take a closer look at the ignition switch with the VOM. You should get a near zero resistence reading across the contacts.