I've used Klaviyo sparingly, so I don't really have any input on it, especially for the SMS function.
However, our marketing department uses it as a primary tool for email marketing. Whenever we encountered any problems with our Klaviyo set-up, we opted to work with a company called CodeCrew that's known for being a Klaviyo Agency.
I'm not sure if they're still doing free consultations, but might be worth sending them a message! Shouldn't take more than 10 minutes, I think.