I had already prepped the old window sill by filling the voids with thickened epoxy. I used System Three epoxy and silica filler from my local Woodcraft store, and was quite pleased with it. They have three different hardeners from which to choose, depending on how fast you want it to cure. The stuff is mixed in a 2:1 resin:hardener ratio, so I bought a quart of resin, a pint of the #2 (medium cure time) hardener, and two quarts of silica thickener. Total cost was about $75. That was enough to repair this window and two more less-needy ones, and I still have about a fourth of the epoxy left over.
Borrowing a page from Roamer46's book, I first wet out the bare wood with unthickened epoxy, using a disposable acid brush. It penetrated the wood surprisingly well (unlike the 5-minute variety that I'm accustomed to) forming a nice waterproof barrier. Then I added the silica thickener to the epoxy, and troweled the resulting paste into the voids, using a disposable wooden paint stirrer. The next morning, after the epoxy had cured, I ground down any high spots with a 60-grit sanding pad on my oscillating multi-tool, and also roughed up the low spots for better adhesion. Then where needed, I used both round and straight saw blades on the multi-tool to re-cut the grooves for the weatherstripping.
The last prep step was to apply and sand ordinary spackling compound, for smooth flat surfaces. Sorry, no pics of the prep stages, as I was in a major hurry to get this thing done.
After all the prep work, actually installing the new sill pieces was a breeze. For the sill plate, I wet out the edges of both the old sill and the replacement plate, stuck them together, and nailed the replacement plate down to the 2x4 underneath. The nose piece went on next using the same process, except it was simply clamped on while the epoxy cured.
The pic below shows the sill with the new pieces already installed and caulked. It was taken at 8:48 AM last Saturday. Notice the red & white tent in the background? My twins' high-school graduation party was scheduled to start at 3:00 PM that very day!
On went a quick coat of latex paint, despite the spackling compound still being a bit soft -- the humidity had been almost 100% overnight. Installing the new sashes took just a few minutes with some help from my son, and we were done by 1:30. Good as new, and ready for the big party, with 90 minutes to spare!