Fractional jet Captain reported very crowded ramp conditions at destination almost resulted in a ground collision.

Narrative

Aircraft X. 91K flight with pax (Passengers) on board. Landed Runway XX. Taxied to ramp via [Taxiway] 1 to 2 and entered the ramp at 3 as directed by FBO marshaler. Ramp was completely full. FBO Marshaler directed us to pull in the taxi lane between two rows of parked planes--jets on the right; propeller planes on the left. There were wing walkers on both wings. It was extremely tight and I told the First Officer (FO) to be prepared to hit the brakes if needed. The front marshaler kept motioning us left then forward. I saw the left wing walkers signal X" to stop but the front marshaler kept signaling us to turn right and continue. Initially the left wing walker gave a "thumbs up" as I was looking out the window; then he immediately gave a "X" as well as a closed fist to signal STOP. The front marshaler kept signaling us to continue moving forward. I looked and could see that our left winglet was not going to clear the prop on the plane on our left so I stopped the plane; set the parking brake; and shut the plane down. We deplaned the pax and luggage and asked the FBO to use their ground equipment to move the plane to a parking place. When they hooked the electro to our plane the base of the winglet was about 12 inches behind the spinner of the propeller plane. There was only approximately three feet between the right winglet and the nose cone of the jet on the right side. They tried to push our plane back but there wasn't enough room on the right side left to straighten it out. So when they pulled our jet forward the they had to have the left wing walker simultaneously rotate the prop of the propeller plane so the left winglet could pass thru the gap between propeller blades without hitting the propeller. Our plane was then towed to a parking spot that had opened up. Suggestions: I spoke with the ramp supervisor and he said "we are so busy today these things happen". I suggested that when the ramp is that full/busy it was the exact time people need to slow down and do their jobs correctly. I also reiterated that the front marshaler has to respect the wing walker signals to stop."