Your problem is not the power of the burner (heat) it is the really thick tip. The high end burners are adjustable over a range of temps (makes it easy to shade colors into the carving) and may allow two burner hook up> They are not necessary. What you need is a burner that has "pens" that hook up to it....basically a writing pen with a tiny little "razorblade" edge. These thin wire tips get hot, do it real quick, and can be kept hot while in use. The other thing is the small tips allow you tight turns, positive control, and allow you to do that "fine" work you see in Pyrogrophy portraits. These units are a control box with a rehostat heat switch, a pen "handle" with fine tips ( they make two types of pens) the first type has "replaceable tips" on a fixed body....the other has a "fixed tip" that is part of the pen body. My experience over many years of use is to stick with the fixed tip type. The replacement tip kind will eventually fail at the "push-in" contact at the pen body....the fixed are part of the unit. When you fire these up that tip can get nearly white hot so "extra" connection points are not a real good idea.
I have a very old unit called "the cub" and is made by a company called "Detailer" that I use with fixed tip pens. At the time it was the cheapest of the so called fancy burners...They still make an entry level burner for about the $50 range. That has been my experience with wood burning, when I was younger the feathers on bird carvings would have as many as 100 burn lines to the inch, heat colored, and the feathers looked absolutely real and soft. That was then and this is now but the point is ya dont need the top dollar ones to do great work. Hope that helps.
rich