So you soften the horn and form it around a round form? When I made one like that I kept it's natural form and fit the plug to it. As I recall I fit the plug first making it small enough to fit down inside the horn then cut away the back part of the horn down to the surface of the plug leaving a tab on top. For fitting the plug I glued a handle on to it so I could easily insert and remove it from the horn while fitting it.
Before you do anything make sure you horn is scrapped thin and shaped. The base kind of depends on what type horn you are making. If you want a round base you will have to heat it, oil/water/heat gun and then tap a sizer in.
Do it before the lobe is cut to shape. Mark a line around the base on the sizer measure the diameter and turn a plug. If you don't have a lathe you can do the same thing, round the horn, square the end, stand it up on a piece of wood and draw around it, make a witness mark on the base, inside the circle and one on the horn. If you have a Band saw tilt the table to about 10 deg and saw out the circle (this will also work if you leave the base natural) If you do not have a band saw a coping saw will do. There is still hand work to do, if you have a disk sander set the table to once again 10 degrees or so. Start at the witness mark and sand around the circle, you will eventually take out your line, Once the plug starts to fit take a soft lead pencil and shade the inside of the horn, keep the witness marks in line, press the wood in, remove and sand the pencil marks off the base. Takes some time, once the base is about half way in you can cut your lobe then continue to fit the base.
I usually use 5/16-1/2" wood for the base with either leave about 1/8" sticking out of the horn, you can catch that edge with a knife and pop the base out. Once it is fitting like you want taper the top edge that is under the lobe, attach the base and work the 1/8" extra down to the horn. I like to make the base domed as some were.
All of this can be done with hand tools, no coping saw, cut the edges off with a hand saw, no Disk sander, rasps and files
Hopefully this is not to confusing and helps.
Tim C.