It's not really like the engine gets more air due to less restrictive exhaust. Think about it, how could it? Only if you fix the airinlet too. And vice-versa.
But, when that's said. You should always control and- or adjust the settings after doing something to the engine.

I started out cutting the airintake on the airbox. Cutting some more and finally throwing it in the bin. Severel types of exhaust, trying this, trying that. Working with the jetting and airmixture along the process. Ending up with no airbox (Pods from Ramair, UK), freeflow exhaust and new jets, pilot 45 and main 140...or 145) I learned alot during the process, but it was a waste of ridingtime!
So what I think you (all) should do is to remove the SAI, open the exhaust with some good pipes, remove the airbox completely and install pods, rejet or remap. Go out and enjoy your "new" bike!

When it comes to pipes, I bought these from www.louis.eu

https://www.louis.eu/artikel/long-universal-exhaust-chrome-38-45-mm-no-tuev/10027110?list=15176403

And a turnup bit between the pipe and the header for that upsweep-style. Drilled 2X10 mm (or was it 3?) holes in the backplate for some more noise and power. Works great! Saves alot of weight too. Those OEM and tors are really heavy! See pictures in the latest (no 14) issue of "Spirit", Triumph's web-magazine. Good luck!