Ok, good it's at least running now..
 
Did you adjust, on the carberator, the HIGH SPEED adjustment screw in to lean out the mix?
It sounds like it's running too rich.  The HS screw is closest to the air filter, away from the cylinder.
 
You'll need a special screw driver to adjust those (if you don't have one).
 A complete set of adjusting screw drivers are on Flea bay for cheap. 
 
Also, does the clutch hub, the outside part, spin freely with the engine off?
 
.

I adjusted the high screw in some.  It just seems to be running rough.  I even adjusted the Low screw some to try to make it stay running or to actually idle.  I am not able to get this to run.  If I continually give it gas it will stay running for some time, but if I let off gas, it will die almost immediately.  The clutch is spinning free with the engine off.  This saw is super clean and appears like new condition.  I do not feel any play in the main shaft at all.  Again, Thank you for your response, and I appreciate the help.
 

I'm running out of tricks for ya..
 
First, as there seems to be a lot of blue smoke(oil), perhaps dump that fuel and re-mix.
 
Second, try running with the air filter off the machine. 
 
Third, try running with the muffler actually removed.
 
I know the machine looks new but try all the above (clogged muffler-ESPECIALLY the screen, clogged air filter-even if it looks good).   All will limit RPMs and performance if compromised..
 
A new spark plug couldn't hurt to try.. I believe .025-.026" should be spec. 
Lastly, R&R the flywheel and check the key way. While there inspect for any leakage around 
the cylinder base gaskets...
 
.

SRTsFZ6
I'm running out of tricks for ya..
 
First, as there seems to be a lot of blue smoke(oil), perhaps dump that fuel and re-mix.
 
Second, try running with the air filter off the machine. 
 
Third, try running with the muffler actually removed.
 
I know the machine looks new but try all the above (clogged muffler-ESPECIALLY the screen, clogged air filter-even if it looks good).   All will limit RPMs and performance if compromised..
 
A new spark plug couldn't hurt to try.. I believe .025-.026" should be spec. 
Lastly, R&R the flywheel and check the key way. While there inspect for any leakage around 
the cylinder base gaskets...
 
.

In the last few weeks, I tore the saw all the way down.  The piston and cylinder look great.  Almost new.  The Muffler screen looks good but I used gas to soak it and then scrubbed it with a tooth brush.  When I had the piston out, I tried to clean the small amount of carbon in the ring channel.  I broke the ring in the process so I replaced the ring.  I lubricated it fully, and rebuilt the saw.  I turned the carb H and L screws in all the way and then out about 1.25 turns.  The saw fires right up, but still runs the same as it did before I started all of this.  I have run it with the muffler off and the air cleaner off.  It still is not running well.  The gasket at the bottom of the cylinder looks great. I am out of ideas. The compression is about 133 psi.
               

Still running like the last video?  Like loading up and smoking alot?
 
.

So I am really out of ideas now.  I tore this saw down again and thought maybe the shaft seals for the lower end may be bad so I replaced them.  I also replaced the gasket on the bottom of the cylinder to make sure it is not a problem with the seal.  The piston looks great, and compression is good.  It seems to be running just like it was before all of this work.  It makes no sense, as this saw looks to have very minimal use.  I just don't know where else to go with this.  I have had 3 different carbs in it with no change.  I replaced the boot from the carb to the cylinder.  I am out of ideas
 

I would put the original carb back on. 
 
I gather the fuel oil mix IS correct (as it does smoke alot)?
 
I looked at the old video again, and I believe it's a fuel related issue running too rich.
 
Try adjusting the HS screw with the throttle wide open.  Don't be afraid to turn it a bunch for now.
Get that excess fuel cleared out.
 
Again, for the LS adjuster, lean out (turn the closest to the engine) clockwise to lean the mix and get a good steady idle...
 
I'd also go thru the carb again, compare pic's with your carb.  
The squareish diaphram, part #34, should be nice and soft, no holes, NOT stiff.
That IS the fuel metering diaphram allowing the correct amount of fuel into it. 
 
I'd also remove the needle, check for any crap in there holding it open/flooding it.
 
https://www.jackssmallengines.com/jacks-parts-lookup/manufacturer/husqvarna/chain-saw/440-e-2009-02/carb-details
 
 
 
 
 

I would put the original carb back on. 
 
I gather the fuel oil mix IS correct (as it does smoke alot)?
 
I looked at the old video again, and I believe it's a fuel related issue running too rich.
 
Try adjusting the HS screw with the throttle wide open.  Don't be afraid to turn it a bunch for now.
Get that excess fuel cleared out.
 
Again, for the LS adjuster, lean out (turn the closest to the engine) clockwise to lean the mix and get a good steady idle...
 
I'd also go thru the carb again, compare pic's with your carb.  
The squareish diaphram, part #34, should be nice and soft, no holes, NOT stiff.
That IS the fuel metering diaphram allowing the correct amount of fuel into it. 
 
I'd also remove the needle, check for any crap in there holding it open/flooding it.

 
 

It sounds like you've tried a lot to fix your 440 chainsaw, but it's still giving you trouble. It's good that the piston seems okay and the compression is decent. Since you've already swapped the carburetor and cleaned it well, maybe check the fuel lines and filter for blockages next. Also, that hammering noise might mean something's up with the engine itself, like worn bearings. If you're stuck, don't hesitate to ask experienced folks or check online forums. Keep going, you'll figure it out!