Monday night I performed about a 95% water change. I took the water level as far down as I could without removing Spartacus. I then added Stress Coat to remove the chlorine and help build back his slime coat. Then I waited for the temperature to drop some (got it a little warmer than usual), and after it came back to around 80-81 degrees, I added the Bio Spira.

I took some readings today and they are:
Ammonia .25-.50 ppm (it was a little hard to tell)
Nitrite .25 ppm
Nitrate 5.0 ppm

So, it is starting to cycle. I added some Stress Zyme and Easy Balance to try and help speed things along, too.

My question is, would it be safe to do a partial water change without interferring with the Bio Spira? Or should it cycle fast enough that I don't need to do a water change just yet?

I don't know much about bio spira, but from my understanding, it is like an instant cycle on your tank.
And it has to be kept in th fridge or freezer.
Because you are getting a reading, I would do a partial, and add the amount of bio spira to the tank to the amount of water you pulled.
You know, 10 gallons = 1 teaspoon
5 gallons = 1/2 teaspoon
2.5 gallons = 1/4 teaspoon.
I am not saying that is the amount you use, I wouldn't know, but if you pulled say 2.5 gallons of water, I would add the equivelant of that amount of bio spira.
Hope I am making sense, and not just rambling.

The Bio Spira was added after I did the 95% water change, on yesterday. I'm getting these readings after I add the Bio Spira (today). I don't have anymore to use.