If the rise is all night, it sounds like your insulin or your site absorption. The only times that happens to me is when I have a pump site problem, so I'd hazard a guess it isn't the lack of night feeds
As I said, I don't remember exactly when I changed my basal (continuing baby brain!!) but I would think that I tweaked it something like 4 times maybe in the first year or so, with most of those tweaks being towards the end of the first year. I'm still feeding now (my son is 2) and I've done a couple more adjustments too.
Hope you get it sorted