Actually with vintage octagonal and round barrel rifles a muzzle clamp and front rest is actually better.  Between 1900 and the start of WW I there were two forms of competition.  Offhand of course and what was termed muzzle rest (what we now call bench rest).

But with the longer action rifles such as the Ballard (in the case of my rifle a Stevens-Pope Ballard) an octagonal clamp is used in a sliding fixture on the front rest.  Because the entire rifle will actually flex if pressure is applied in the vicinity of the action.  

Trying to support this type of rifle by only its forearm (or just in front of the forearm) would lead to muzzle whip and an erratic change in point of impact.  You will see greater accuracy at 200 yards with a muzzle clamp.  This is not to say you cannot rest the barrel on a sandbag.  But, if you quest is for the greatest accuracy then a barrel clamp is what you want to use.  Sometimes called a "bobsled."  

If you have access to Randy Wright's "Loading and Shooting Traditional Schuetzen Rifles - A Beginner's Guide" refer to pages 80 -89.  Also refer to Dell & Schwartz "The Modern Schuetzen Rifle (1999)" chapter 12B page 244.

I do not have the muzzle rest my Grandfather used with his rifle because it was sold to a friend of his in the 1960's.  

Refer to ASSRA Rule Book:

Section 2.91 Sandbags and Rests
 
A sandbag or shaped rear rest sand filled bag made of leather or canvas may be used under the toe of the buttstock. No other device or support is permitted for the toe of the rifle. V-blocks or rests, guides, ways, or any such devices which may aid in alignment and realignment of the rifle, are prohibited. An anti-cant device (bob-sled) similar to the Pope style muzzle rest or the one described in Mann’s book is permitted. Also a spirit level or sight attached to the barrel is permitted. A simple stop may be attached to the front rest as an aid in realigning the rifle for the next shot.

In terms of pure accuracy, has any method been definitively established as the best practice?

To some extent position on the rest is dictated by what you are doing with the rifle. Many shooters using cross sticks, LRBPC etc., believe that placing the barrel on the sticks gives them the best control for aiming. A major consideration in this method on stick or with a bench rest is the determination of the vibrational node closest to the muzzle. Resting on this point or attaching a sled there is critical according to most people. My own personal experience has not clearly established one method as superior to the other with the BPCR rifles I shoot most frequently.

 Or is it an empirical question with each rifle being a law unto itself?

Yep, more or less try it and find out. I suspect that the two piece stock common to most single shot rifles is a factor in this and that is why it's not common practice with 'normal' benchrest shooting.

Does it matter whether it is a .22 or other mild caliber, or something with more recoil?

I don't know how important barrel weight is in this equation but I suspect that the lightest contours would not react well to the techniques. The heavy slow bullets used in a great many single shots produce quite a bit of torque and the  sled minimizes or eliminates it.

While I was writng this stebbinsgr posted so I guess a lot of this is redundant.

Very interesting Info.
I also will be testing the effects of a front barrel rest next year when the weather gets nice. Most all of my testing will be with a Ruger # 1 in 22 LR being I have one of known accuracy when shooting off the forend.

Will also try it on my 32-40 as I haven't gotten very good accuracy with it shooting off the forend but I'm sure it's a lead bullet problem because it shoots jacked bullets great, but if it shoots better off a barrel rest then I'll know it helped. 

I think a lot of the accuracy problems is because most traditional Schutzen rifles have two piece stocks,  whereas most modern bolt rifles have a one piece stock and a better way of attaching the stock to the barreled action.

I have been noticing that most barrel rest are attached between 6 and 8 inches from the muzzle, I'm wondering if these barrel rest are acting more like a barrel tuner and moving it up and down the barrel I'm sure is having an affect on the accuracy. 

It will be interesting to see just how much movement it takes to affect or improve accuracy. My understanding is that in ASSRA matches barrel tuners are NOT allowed but these muzzle rest are, even thought they can act and be used like a barrel tuner ?,  or is there a rule that a barrel rest has to be a certain distance from the muzzle, that of course would probably prevent them from being used as a barrel tuner.
  S T

Joe:

I have found that the best rests usually involve at least 8 hours of interrupted sleep!!!

Jeff

I use a bob sled but I must say some of my best shooting has come from resting the barrel on a 6 inch x 6 inch pillow bag filled with heavy sand and yet keeping it as soft as possible The only down side of using a pillow bag is you have to master control over torque and recoil. Out my way if you drop a point you won't make it into the top three so I currently use what gives me the best consistency and not necessarily what gives me the best groups if that makes since.

Hi J Louis,
Have you noticed just where or how many inches back from the muzzle you are resting your gun. Like I've said in one of my post, most that I've seen pictures of seem to be about 6 to 8 inches back from the muzzle. I'm sure this will vary with each gun but just curious. 
S T

One problem I find with the muzzle rest, ( bobsled ) is finding a bench long enough.  At the range in Poulsbo I would have to make some kind of extension to clamp to the front of the bench to set my rest on. Seems most benches are made for bolt guns and repeaters and other such rifraf.

Come to think of it I dont know of any range with benches long enough. I remember watching Ron Long shoot a very heavy 38/55 Ballard with a barrel rest at the range at Cody Wyoming. The buttstock extended quite a way past the end of the bench. Ron didnt look very comfortable shooting it. 

                            Joe.