There is no need to do any converting or add/subtract. There are differences between all meters (ie. no two meters will give identical results) the essence of measuring BG and treatment is not about absolute accuracy but rather "ranges" like the colors on our spreadsheets indicate.
As with any scientific data collection experiment it is always best to try and limit the number of variables, which is why we say pick a meter, use it, and don't try to make comparisons or adjustments. Accuracy is not as important as precision (accuracy is how close a value is to the actual "truth", precision is the degree to which repeated measurements under unchanged conditions show the same results. Things can be accurate but not precise, precise but not accurate, neither, or both. You trust the speedometer in your car most of the time but it is likely not 100% accurate, it should be precise though. When you are actually driving 58 MPH your speedometer always shows 55MPH, it is not accurate but it is precise and for that reason almost every measurement device has an industry accepted allowable varience or error margin. You won't get a ticket for speeding when the police radar measures 58 MPH in a 55 zone, speedometer varience is allowed as well as the fact the radar is as well not 100% accurate.
I don't know which insulin you are using but the protocol for Lantus and Levemir specify ranges and dosage changes based on BG results measured on a human meter (eg. Relion, Freestyle...) The Alpha Trac is not more accurate than any other meter, though it is calibrated for felines it does not make it "better" or more reliable. It is significantly more expensive and therefore less useful (when you afford to test often enough, or have difficulty purchasing strips), using a human meter with which you are comfortable with and can afford and good availbilty of strips etc. is going to better than worrying about any "differences".
I suggest you use the Relion, make a note on your spreadsheet that you changed meters and don't worry about making any comparisons, your data collection begins anew with the meter change. If the number was 393 it's to high period, does it really matter if it's 350 or 450, in either case the cat needs insulin!
As with any test a single measurement is useless, rather it is accurate or not, more important is the trend of repeated measurements over a short or long period of time. In treating diabetes we are more interested in being in the right "zip code", not the exact " house number" ;-)
ETA: The way to improve accuracy is by increasing the sample number (more test results) this will correct any possible "error" values.
If I average the numbers 50+100+450and divide by 3, I get 200
If I have a larger sample 50+100+450+75+90+110 and divide by 6, I get 145 which is both more accurate and more precise.