Something is making this way too hard. look at this http://www.cdagro.com/dip/dpo.html
If you put your antenna into an inverted V configuration multiply each side by .95 as it will be 5% shorter.
make sure you you don't have anything shorting the inner conductor and shield, make sure that the centers and ends of the dipole are insulated and go for it.
Your TS520S according to the specification will tune 50-75 ohms, in reality it will tune from about 30-350 ohms impedance with no problem. Been there and had one, a good radio.
Cut your dipole according to the dimensions provided by the calculator, put the SWR meter on the shelf, and start using the radio. WAY WAY too much emphases is being placed on a low SWR. I would have stopped at 3:1 that you had, unless you have a very long feed line, that is not a problem for the 520S. You are not using a modern radio where SWR is a problem.
Here is how I see it, you are young, and have a lot to learn on antenna theory. Get your dipole up as high and in the clear as you can. Read the 520S manual on how to load it, and start having some fun.
Modify things as you start to learn.. The 520S has a SWR meter built in if you care.
35 years ago most hams did not have an SWR meter and made thousands of contacts. Today people think that if the SWR is not 1:1 you can't make any contacts, that though process is rubbish...
Have.. fun.. Fred