That is the right/best size tubing.

If your hose fixtures are too big, you might be able to make them work. Heat the tips of the hose in boiling water for a minute or two.. this softens the plastic and you might be able to stretch it over the barbs. Depends on just how bad the ID mismatch is at the barb.

The reason length is being talked about is that it's the the only variable that doesn't effect something else.

- beer pressure should be by beer style.. belgian beers are way more carbonated than porters, etc..
- temperature you're going to set and multiple beers will have to live with it
- pour rate should probably not be faster than a pint in ~5 seconds for foamig

I have a short line for cask style, super long for carbonated water (dabble in soda syrups as well).

Also, is there a home brew shop in your town? They will have all these parts there if you are now backed into a corner time wise. Maybe can get 3/16 fittings if stretch trick doesn't work or they will have 1/4 ID food safe hose as well but then you prob want 20 feet.

The other thing is have you moved your thermo stat to the keg itself? Tape it to the side of the keg.. turn the fridge to Max. That will help your fridge out a lot and get you what you want. And add fan up into tower as people suggesting.

I hadn't seen this one before, very nice. I had a spreadsheet I got somewhere that was way too optimistic, this one looks closer to my real world experience