If you have the reamer you can make your own forming dies quite easily, take a cast off barrel at least 7/8" diameter thread it to 7/8x14. Chuck the threaded piece or better yet a collet, pre drill a hole that will allow the bushing to pass through if the caliber of the barrel is less than 7 mm. Use the reamer to cut in until about 3/4" of the brass body is cut. Once the reaming is done you can bore the neck out to a desired size. I usually do both ends of the threaded piece. Make enough of these neck forming dies in graduate sizes so you can gradually neck down the brass, to keep the brass from buckling by trying to take the neck size down too much in one pass.
Granted these forming dies will not be hardened so you should take extra caution to see to it that your brass is clean before sizing, any grit will scratch the unhardened dies. In addition the dies will wear far faster than regular dies, but that should not be a problem as you will probably not size enough brass from necks of .611 to .375 that the wear will a problem. In addition, the final sizing will be done by the actual resizing die you have and that should reduce the neck and shoulder region as it will be smaller than the dies made by your chamber reamer.
I saw a great video of a Scandinavian gentleman make dies and he chucked up a piece of stick in the lathe and cut internal threads at 7/8x14 and did all of the machining of the die blanks by threading them into the piece that was internally threaded without removing the piece from the chuck. The steps of threading a sacrificial piece of stock and not removing it from the chuck is done to maintain good concentricity between the OD and inside of the die, since you are not cutting the final die threading a piece to accept the die body may not be needed, but if you want to do all that you can without having collets it works pretty good I have used it for any number of similar tasks.
I am not a machinist and don't claim to be, there may be some steps that I have missed or were not done to a high level of skill or technique but I will say this I have cut neck reducing dies twice using this method and the results worked great. The machinists amongst you can probably make suggestions for better machining techniques than I laid and I ask you to make them, like I said I am not a machinist.
I made dies this way to reduce the necks from 375 Ruger done to 300 for my 300-375 Ruger years before the 300 PRC came out and for reducing the neck from .264 to ,224 on my .22 x 47 Lapua. In both cases the resulting cartridges were as accurate as I would expect.
Hope this helps,
wade