I have run across a bore lapping kit by Wheeler. Includes three grits and a couple small steel plates. Use involves pressure-rolling bullets across a plate covered with one of the three grits, impregnating bullet with grit, wiping off excess grit, and firing bullet. Will those with experience with this approach please comment on it? Thanks in advance.

It's called fire lapping. Not a controlled lapping process. In frustration I used it once to remove burrs in a newly re-bore barrel and it worked good. Thinking I fired ten shots with grinding compound on the bullets. 

No kit, just rolled the bullets on Clover grinding compound.

I've done a fair amount of fire lapping.  Always on barrels that have problems, either rust pits/roughness, possible throat burrs in newly chambered barrels or barrels that "look OK" but for some reason don't seem to shoot as well as the looks suggest.

Merrill Martin developed the process and wrote it up in detail in the old Precision Shooting magazine.  I follow his procedure rather than those of the later innovators that claim it ruins barrels, and (typically only when pressed for details) then describe their own processes, which often feature the use of jacketed bullets, full loads, the firing of whole boxes of treated ammo machine-gun style and so forth.  I've never tried it on a barrel that shoots well already, and I've never made a barrel shoot worse by doing so.

Properly done, it's no more damaging than the lapping one would do with a detached barrel and a rod with a cast lead lap.  (That process, need one say it, can ruin a barrel as well if not done right.)   Each shot is one "lapping stroke," if done properly.

Many years ago I read an article on fire lapping where the writer used different valve lapping compounds on the tips of the bullets and fired them down the bore of a rifle. He recommended firing 5 shots then thoroughly cleaning and scoping the bore. Then repeat as needed until it was smooth.
I tried his method on an old dark bore and it turned shiny after a couple 5 round strings. I then shot a second group after cleaning, and my groups were smaller than before. I'd never do this with a new barrel as it's not really controllable, but it did make my old bore good enough that I chose not to reline it.

If a little firelapping helps it doesn't mean more is better.  Too much can damage a bore.  I've firelapped several barrels some time ago, including some that were lighted pitted, rusted or were prone to bore leading.  Just understand that besides smoothing the bore it will definitely extend the throat as the lapping compound wears the leading edge of the lands.

Wayne

If I do it, I will take my borescope and laptop to the range to observer the results real time. My scope won't work with my phone.  No power available.

I tried fire lapping with a Hepburn in .40/50 SS with a pitted, dark bore that still had decent rifling and a HW in .32/40 with the same type of problem. Both shot poorly & leaded up quickly. Pushing a cloth cleaning patch through them met with a fair degree of resistance. I used soft lead slugs that were slightly over groove dia. and rolled them between steel plates with 360 &  500 grit sizes (silicon carbide lapping compound in oil). Fired 2 x 3 shot strings with the 360 and then 5 x 3 with the 500,  cleaning between each 3 shots. Used a load that gave about 700 fps. This resulted a much improved shiny bores in both that were noticeably smoother &  shot quite well with hunting loads and they were a lot easier to clean.
As others have noted - don't overdo it and it will probably improve a old tired bore.
Spud