Mounting the front light on the frame instead of the fork or the handlebar?

The lag is an issue, even at low speed (even more, I would say, because your wheel and handlebar will turn, while at high speed as in the video you posted the bike is going as a whole in a certain direction).

If you are on rocky road, you will soon discover how annoying is trying to avoid rocks/ruts that are partially in the shadows.

I had some luck in searching the internet with for the words "Bike Stem front Light" in finding some less bulky solutions that may appeal you.

If you wear a helmet, putting it on the helmet may be a solution (no diy solutions, if you know the rumours about the skiing accident of Michael Schumacher you may imagine what can possibly happen, having an object that can penetrate the helmet attached to it ... nail and hammer ... and you are the anvil).

The light is better on your handlebars or fork than on your frame - the frame lags and always points at some tangent to where you're going while turning, so either you need a really wide beam, or you have to ride into the dark.

Fortunately there are solutions, and some of them are pretty vintage.

1. Steerer mount. In the days of threaded headsets, there was a stack of anti-rotation washers needed. It was common for one of these to be extended out the front and upward, to support a "bicycle lantern"
   As time went on these changed from oil lanterns to battery powered by two D cells.

this last one is a particularly vintage unit, but shows how it is mounted on the bike, below the threaded stem's retainer nut.

2. A variation on the above is to mount the lamp from the front wheel's brake bolt.
   Downside of this is its getting quite low and can be obscured by wires. Also many brakes don't have bolts long enough to go through more thickness. However if your bike has a cantilever, V, or disk brake, then this hole is either spare or used only for a mudguard/fender. Worth considering.

3. There are a ton of options for mounting things under the bars too, which helps clean up your working area. Risk here is that some lights are built with a certain intentional beam pattern, and flipping them will light up other road users in an non-legal manner.

If you have to mount your light to your frame, there are two ways to do it.

1. Secure a longer flashlight/torch to the side of your top tube, such the front lens area is forward of the head tube. Downside, a torch makes for a bad headlight because the beam pattern is wrong.

2. Get a gopro handlebar mount, and put it around your headtube with the clamp between the top and downtubes. This will let you use some kind of gopro to your-light adapter.
   I use this for my gopro on an older road bike, and the footage is really directional, makes me look quite pro while riding.

What I would do is braze on a rack-mount lug. Or you could braze on a water bottle type of boss, and a short bolt, and the light would mount using the standard mount for a fork crown.

I mean to braze a lug onto the head tube of the bike. Brazing would only work on a steel frame. There's no need for anything to intrude into the head tube if you braze a lug on. I am considering this solution myself because I also don't like the light wagging back and forth, especially while climbing.

I already have a helmet light for curves, and my front light also hits the front fender and leaves too much shadow. The other idea is to 3D print a mounting block.

This is a product that Peter White Cycles calls a "nob." It's an accessory mount that can fit around a fork blade (something like this is also often used on aerobars). Which is not what you want, since the fork obviously turns. However, it might fit around the head tube, or give you an idea for a homemade equivalent with PVC and zipties.