I am most impressed by your endless ingenuity!!!
If I could not throw you off course by pointing out the gears in your link were not bevel gears, let me put another factor before you.
Torque rating of your new gears. I know you said the gears have 16 teeth but no mention if they were steel or cast iron. Also no mention of the thickness or width of the gear.
The spec's for your tractor say 11 pto HP at 540 rpm.
To select a gear you need to know how much torque it has to transmit.
I used the "on line," calculator shown below to determine your rear pto is putting out 107 ft-lbs of torque. On the calculator result it talks about engine horsepower but you are only concerned with pto horsepower.
Next I went to a gear design program. I said your gear had 16 teeth, made of high quality steel and would be 1" wide or thick.
Next the program takes the gear parameters and determines the torque level that this gear will sustain reliably.
The important data for your application is "Load in inch lbs @ pitch line which is 581.4. Now this needs to be converted from inch pounds to foot pounds by dividing by 12
Now the torque number is 48 ft-lbs which is less than 1/2 that your pto puts out.
I want you to succeed not fail and you need to know what you are doing will not withstand the torque from the rear pto even with a gear 1" thick which your's is not based upon the photo.
If you are wondering why such a big challenge, it is transmitting the torque at 540 rpm's.
A 1,000 rpm pto speed would basically double the torque capacity of the gear.
Unfortunately, you don't have that pto speed.
Driving something off the front of your engine which runs at say 2,200 rpm makes a very big improvement for a gear's ability to transmit torque.
I know this is all very technical and not many would understand the intricate details. This is the manner which my engineering background has me approach a technical problem.
Please feel free to ask questions. I will do my best to answer them. I am not a power transmission specialist but rather a generalist. Power Transmission people make that aspect of a machine's design their life long career.
Dave M7040