You can also "return" the shoe; round over the top of a square cut so it appears to miter back into the baseboard. It looks a little classier than the 45 (we usually use 40 degree) end cut.
Anyway, yes a japanese saw (I use a fine dovetail saw with an .012" kerf) will make a perfect cut in place. But it's a quick way to ruin a very nice tool sawing paint, finding embedded nails and some plaster.
The plinth stock should be no thicker than you need, and often is looks best to bevel it some amount so it is thinner at the door-edge side of the casing, to better follow the profile of the casing. Rectangular-section blocks are only appropriate for casing that is symmetrical down the centerline; equally thick at either edge.
Some lumberyards carry 1 or 2 styles of plinth stock, otherwise you get some 6/4 material and play with the tablesaw or plane.
Casey

Trim carpenters often use a "MultiMaster" for this type of cut. (See link).

Since Fein's patent recently ran out, there are a bunch of competitors with new tools -- Bosch, Dremel, Rockwell, even Harbor Freight have lower cost versions if you are not wanting the spend the money for the top of the line model. The accessories (blades) seem to be interchangeable.

Here is a link that might be useful: Multi-Master

If you put a plinth on the bottom, you might have to put a plinth on the top so it doesn't look odd. If it were me, I would measure the amount the shoe molding is proud of the casing, remove the casing, and then use strips of backer to bring the casing to the correct thickness, or get or make new casing thick enough to accommodate the shoe molding. Any way you do it I believe the amount of work will be about the same unless you do the return, like Casey said.

All great ideas - thanks, everyone. Another possibilitiy - instead of the plinth approach - might be to remove the section of baseboard on either side of doors, add a backband piece all around the door casing as a buildup piece, cut the ends of the baseboard and fit it back onto the wall and tight to the new casing backband; and then add the shoe mold to the baseboard. Assuming that I use backband that will project enough to receive the shoe mold -- this should work...right?? Only problem with this approach is that the door casings will now be diff than the window casings. What do you think??

"If you put a plinth on the bottom, you might have to put a plinth on the top so it doesn't look odd."

Using a bottom plinth only has been SOP for about a few hundred years.
Nothing is required at the top of the casing.

Plinths are often plainer than the remaining molding.
They just add enough thickness to ensure that base and shoe do not protrude past the edge of the door casing.

Yeah, I'm sure your mitered picture frame molding with plinths on the bottom look real nice.

A backband on the door without having one on the windows would look fine.

"Yeah, I'm sure your mitered picture frame molding with plinths on the bottom look real nice."

The pieces at the top are called corner blocks, and only are used in a couple styles of molding.

Classically they had rosettes cut in the exact same pattern as the rest of the casing with reeding of variouse shapes and spacing.

You can still purchase matched sets of bits to form the casing moldings and the matching rosette for the corner blocks.

I'd also never heard of using plinths with mitred casings until Casey mentioned it (done differently) in the first response. But I am also not sure it would look so hot.

What exactly is making you want to add a base shoe? It seems to me it's creating a whole lot of huge trouble, and I wonder if there isn't an easier way to solve the problem that the base shoe is meant to address.

Before you sacrifice every doorway in the house, look at the original problem again and see if there isn't another solution.

I'm not a fan of base shoe moulding at all anyway, it makes furniture sit too far from the wall.

KarinL

karinl, -- reason I want to add shoe mold is because old maple floors are uneven in many places, showing gaps betw floor and baseboard (the orig reason shoe mold was used in the olde days, I think). Adding the shoe mold (more flex) will cover the gaps and make things look nice and trim. Thanks to all of you for your ideas! I think I'm going with adding backband to door casings.

Have you thought of just using filler in the gaps? We have this all over the house too. We're still pondering between maybe clear latex and wood-coloured, could use filler too. But I sure wouldn't add a shoe and redo all the casings just to eliminate a couple of spider hiding places :-)

You can also get even smaller moulding profiles than a base shoe, might be so unobtrusive you wouldn't have to worry about the casings.

KarinL