I have the SB V3 for a few years now. I suggest you remove the air duct you are referring to prior to installation. This gives you more hand room to work around. It requires a core workout and the bigger you are, the harder it is to be under that footwell. You can remove the driver seat if you need to. The connection between the sprint booster and your factory connector should be a clean and snug fit. Use the clips on the SB as your guideline. It should go pass the plastic anchors on the factory connector. Make sure you install it right. If the connection isn't flush then you didn't do it right.
Warning: Make sure the connection is a snug fit. It will go in and took me a few tries in a few separate occasions to finally get it done right. If your connection is loose, it is very dangerous. My experience like yours was it lost throttle response once and I had to get off the road and remove the SB on the spot. This was not pleasant with passing cars on a narrow road. The most dangerous experience I had was when I pulled out of a gas station in a very busy avenue and my car went from 0-60 in 2nd gear off the line before losing throttle response. My throttle jumped to almost 7K rpm after I shift to 2nd gear and gave it some gas from first gear. Luckily there were no cars ahead of my path. This messed up my MAF sensor which threw on the CEL. I had to replace the MAF sensor. This is all due to a simple user error installation. I thought the connection was snug too perhaps like you.
Here is the link to install one.
https://rennlist.com/forums/boxster-and-boxster-s-986-forum/518400-sprint-booster-install-on-a-986-a.html#post6818295
If everything is done right and you're still getting this issue with the throttle response then perhaps it's a faulty unit. Good luck.