Based on what I have learned about Honda's 250r's over the years, and building up my own shown in my avatar pic that is running the same 350 big bore that Spencerpaving is running on his saw but with slightly less carb and not being drag ported.. I would say that 55hp is very realistic, if not a conservative estimate of what his saw is putting out.
Just as a for instance and not intending to jack the thread, but I own another '85 ATC250r just like the one in my pic.. It is a stock engine with just the usual bolt-on mods, ie better carb, exhaust, and reedblock. In bone stock config, a 250r was stated to be right around 36hp. You could reasonably expect to be close to 40 with descent bolt-ons, and a bolt-on modded 250r is nothing to scoff at, but the modded 350 big bore R makes the other feel slow! And I am not exaggerating one bit. I have seen dyno sheets from an ESR 310 (which is 295cc actual on it's first bore) with similar add-ons as my 350, except a smaller carb and different brand of pipe, Paul Turner if I recall... That motor peaked out at 49 hp. So yes, I would say 55-60 hp pretty easy on his drag ported 350cc saw.
That thing RIPS Spencerpaving!!! Thanks for sharing the vid!