Have no experience with Slow N Sear, so not much below relates to your question.
Much depends on how well your vents and lid seal, because at some point you can't compensate by shutting things down more if your shit's broke. Windy conditions will blow air into the kettle the kick start coals a few degrees. Or non-equal coals distribution will do likewise as things catch at different times and rates. Hey man, it's cooking with live fire, not an electric range!
I can't speak for others but my kettle temp swings are indeed minor once it's settled down.
"It still seemed that the temp climbed no matter what I did after that. The temp climbed slowly maybe a degree or 2 every 10-15min but it did rise."
Arranging in a snake is a perfect method in the kettle because fresh coals light slowly and replace the spent. This is different from adding either pre-lit or stone-cold coals IMO, where both the coals and lid opening will induce more temp swings. But overall, yes, temps should stabilize and not rise and rise and rise unless there's an air leak or too many coals are being lit inside the kettle. Explore both possibilities.