Dale's my 32-40 CPA Schuetzen Jr. / often times referred to as the Model 52 has severed me extremely well for that same exact purpose It's easy to work on and the parts are readily available or I should say replaced free for life. If you head in that direction shy away from the through bolt and I will share my fix to you for keeping the tang screws from continually backing out as is quite typical of simply the screw design that is being used. That rifle has met and exceeded every goal I have set for myself over the past seventeen years and the first being the same goal you are now wanting to set for yourself. 

JLouis

Dale's if you are planning to shoot off the barrel I would highly recommend that you have a custom front sand bag made to fit your barrel. David at Protektor USA made the one below for me send me a PM if you would like to know the demensions etc. and at the time it was only about forty dollars filled and I had it within seven days. For me just the bag alone has played a real big part in my success and still does. All of the off the shelf bags I found turned out to be pretty much useless for my intended purpose and they were all about the same price as having this one made. 

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JLouis

1885 Winchester High Wall with set trigger, coil hammer spring, forearm hanger, skeletonized hammer, bushed Neidner firing pin, and stock through bolt fastener will make a competitive bench rifle but with a bit slower lock time than the Miller.

All the traditional rifles with a hammer will have a slower lock time than the striker type Miller action.

But by the time you pay for the gunsmithing you can buy another Miller.

Dales
As a traditional rifle shooter of several decades, following are a few of my suggestions for building a BR rifle that should be competitive with anyone you come up against. A successful BR rifle is more than the rifle, it requires a system approach. This system includes the rifle , sights and rest.
Of the actions you mentioned, I recommend the Borchardt due to its fast lock time and throughbolt stock mounting but don’t rule out a Win High Wall. MVA has new made actions that can be had with pistol grip and double set trigger lower tang.
-buttstock with high comb, similar in profile to the Ballard No.7 stock (Long Range model) would work well
-mount your action to the buttstock with a throughbolt for good solid action-buttstock joint
-slim forestock, as you stated you will be using a sled
-32-40 caliber, you did say a TRADITIONAL rifle
-1 1/8 inch (or there about) diameter barrel, 28-30 inches long, round profile, no taper
-for traditional rifle you will need an externally adjustable scope, I suggest a Unertl or Lyman STS of at least 20X, more is better. I use both brands and don’t have a preference.
-Sinclair Competition front rest or similar, they are big and heavy
-Edgewood or equivalent rear bag packed rock hard (including ears) with heavy sand

The only issue with the Borchardt is the trigger and what it lacks the lock time and the through bolt just simply cannot ever make up. The problem with the Miller if you don't have the right extractor for the cartridge you intend to use you might not ever find it a friend has been going through that search for quite sometime. And because of the way it works and quite untypical of the others its also a real challenge to make from scratch. I have no experience with a Hepburn so not to vary away from what you already clearly stated as having on hand to work with of which is already taking place the 441/2 or CPA would be my own personal first choice. The Borchardt my second only if you cannot find a good replacement set trigger for it of which I believe BRC still offers and if so it could easily bump it up to being the very best first choice if its in the budget and still available it's no longer being shown on the Web Site? 

JLouis

Dale's I would first check with both the ASSRA and the ISSA before hand I cannot answer that question in all honesty. And after your comments on your Borchardt triggers it would indeed be a first choice for myself.

The CPA is a bit hard to describe there is a block between the upper and lower tangs, side clearance along the tangs generous ending up with minimal stock to action contact points basically being just the two little cheeks being left after the center of the area between the two tangs is milled out to go past the block. The steel block between the tangs is not real substantial so when the through bolt is tightened as should be that block bends and it then bends the lower tang upsetting the geometry of the triggers. The screws attaching the lower tang to the action should be able to keep the lower tang from bending but from my own experience they have not. 

i hope that makes sense.
JLouis