The right tool for the job

Some time ago, while surfing ebay for tool shopping, I purchased a rebate plane with a convex bottom. What use could it have for me?
Tools not for a daily use for a carpenter or cabinet maker, these planes were in the past may be more used by coach makers and wheelwrights, transportation in which curved elements did not lack.
As in other compass planes, the sole has not a regular curvature ray, rather it decreases toward the toe in order to facilitate the work on curves with a slightly variable ray.
 

The wood is mahogany and it seems a self-builded plane, although very best made and with a very nice rear side.  
Here is the occasion for using it: a first try for building a plane bun with a couple of curved rabbets.

The marked part has to be cut away, but the bottom line is not stright, rather curved. Of course, most of wood is cut away by a saw....

......but a little part of the waste remains:

By using the higher nose curvature and after a short learning curve for the right movement, the job can be completed in less than a minute and with a very good finish.

The dark side of this plane, for me, is the wood of which it is made.
Mahogany wood wears rapidly and is not the best for a plane in which often only a portion of sole is used.
From the image is evident that the wear will be rapid and not uniform.
I am thinking of add a new sole with a harder wood.