I've always used straight barrels on the rifles I've built . . . but, mainly due to the cost of a straight barrel versus a swamped one.
First . . . I got in to using .36 for squirrels (why - don't really know) but I will say that I think the .40 is a nice caliber and pretty ideal for small game as well as general shooting. I've used the 13/16 in .40 and it makes a nice balanced rifle - nothing wrong with it.
That being said, I have handled a number of rifles down at Friendship with swamped barrels and WOW! Most were larger caliber - 50/54/58 and of course larger than 13/16. The swamped barrel just feels better - balance wise. This goes for all of them that I've handled from shorter barrels to longer barrels.
As far as inletting them - if you are buying a pre-inlet stock, I think that you can get them done for a swamped barrel depending upon the source you are using. If not - if you have the ability to use a "blank" and do the inletting, if you take your time you should be able to do a swamped barrel. Just remember to use the widest measurement of the barrel to determine the location of the ramrod channel and for boring the ramrod hole.
It sounds like a great project you're going to do. I got to know Myron Carlson at Friendship years ago - he specialized in iron furniture for Bean rifles, etc. and had also made a number of miniatures. Unfortunately, he is now gone but I remember his Beans and I picked up a 3/4" X 42" - .36 caliber to make one - hopefully later this winter. I picked up two stock blanks from a guy from Kentucky that are "persimmon" - harder than heck but will be nice when finished and very appropriate for a plain Bean. I was hoping to get the 3/4" barrel in .40 but had to settle on the .36. Another reason that I like the .40 is that you have the option of using a larger ramrod (3/8") over the 5/16" for the .36. I've broken several of the 5/16 ramrods but never have had a problem with the 3/8".
If a pair of '51 Navies were good enough for Billy Hickok, then a single Navy on my right hip is good enough for me . . . besides . . . I'm probably only half as good as he was anyways. Hiram's Rangers Badge #63