Older Gravely mowers are picky about blade choices and deck setup. Some of the older deck designs have smaller discharge openings. Gravely mower decks perform best when they are completely level all around or 1/8" higher in the rear. Aftermarket notched high lift blades work best on Gravely mowers.
I had a Gravely with the Kohler ZT740. It would crank and crank but never fire. I checked everything over except the the actual butterfly. Everything checked out. I put my hand over the intake horn and it fired right off. The choke linkage on the carburetor butterfly was broken.
Yes, you could have a spindle problem.
Do the left and right blades both make contact with the center blade?
Does your deck show any deformation around the spindles?
How bad can the cheapo Amazon carbs be? It's a crap shoot. If you are planning on keeping the mower, put on a Briggs carburetor. You will thank yourself later.
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The longer version of either color will capture more particulate.
There are better filters than B&S, Kohler, or Kawasaki. All three engine manufacturers outsource their oil filter manufacturing to the lowest bidder.
I suggest that you get the B&S carburetor. It's a crap shoot with aftermarket stuff.
Replace all of your fuel lines and your fuel filter. Adjust the valves after fitting the new head gasket.
I don't think that will have too much of a problem with setting up your carburetor.
I believe that this is your carburetor. Some of the others on here can confirm.
https://shop.briggsandstratton.com/products/briggs-and-stratton-593432-carburetor
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