Sorry, lol, I cheated because I'm lazy and used awarp calculator. Out of curiosity, are you basing your calculations off the TOS speed? It's very similar to your top speed if I choose that criteria, but I originally chose the TNG criteria which is apparently faster...?
Also, I'm going to wait to see what your laser message says before posting any details, lol, don't want to spoil your thunder!
Not a problem Alex. Actually instead of using a calc and reading the Warp Factor charts on Memory Alpha I went by Gene Roddenberry and Star Trek Voyager. Roddenberry didn't want the TNG vessels to travel any faster than 1000c as the top speed, for some reason. Also in VOY the Intrepid Class starship, which was the fastest at the time was 70,000 light years from Earth and a max warp would take 70 years to get back. 70,000 divided by 70 equals 1000. So in one year Voyager can travel 1000 light years. Meaning its top speed is 1000 times the speed of light. 1000 divided by 365.25 equals 2.75. So Voyager can achieve 2.75 light years per day.
Although many fans and the later Technical Manuals would say other wise, they really didn't work out a true speed when at warp in TOS, therefore there were many instances where the origin Enterprise was actually much faster than the Galaxy Class, but this has largely been ignored/over written by fans and later franchise works. It wasn't until TNG that Gene really said "this is how fast they can go". Michael Okuda did a wonderful job trying to maintain a form of continuity. Naturally it was largely ignore by J.J. Abrams who is a Star Wars fan and thought that warpspeed should be much faster than even the TNG era. Interestingly he probably has a point, for in physics, space does not have a speed limit, only matter and energy travelling through space has a speed limit. 300,000 km/s.