Just to make sure we are on the same page, all the new integrateds I suggested above can meet your requirements to handle two sets of speakers. I am not sure that a separate pre and two separate amps is the most elegant or highest performing solution for a budget up to $2K. Here are some other ideas that I think would work very well, and a couple that follow your suggestion. This level of electronics is more suited to your application and will be rewarded by the Forests. I could not figure out how to make a Naim amp work in this configuration and price range, but if a dealer can figure it out, I strongly recommend you check out the Nait 5i integrated.
Some new Integrated Amps between $1300 and $2000 that can handle two sets of speakers and would pair well with the Forests:
-Creek Evolution 5350 Integrated - nice amp, good resolution without being sharp
-Vincent Audio - SV-236 MKII - Hybrid Stereo Integrated Amp - excellent and powerful amp with a touch of tubes
-Exposure 3010s Integrated Amplifier - another good amp
-NAD C-375BEE - still punches way over $1300 price tag
-Cambridge Audio 840AV2 Integrated Amplifier - good amp, like with 740C I expect this model to be replaced and soon be available at steep discount.
Integrated amp with one set of speaker terminals, pre-out connection and an additional outboard amp:
-Simaudio MOON i-1 Integrated Amplifier plus Parasound Zamp v.3 Two Channel Zone Amplifier
Your 3-box solution - I actually think these might work well:
-Parasound - Halo P3 Balanced Preamplifier, Odyssey Khartgo amp (request balanced inputs) to drive the Totems and run RCA connectors from preamp to Parasound Zamp v.3 Two Channel Zone Amplifier for the kitchen speakers
or
-Parasound - Halo P3 Balanced Preamplifier, Parasound - Halo A23 Balanced Amplifier (run all balanced) for Totems, and run RCA connectors from preamp to Parasound Zamp v.3 Two Channel Zone Amplifier for the kitchen speakers (this combination a little over your budget if bought new).
Remember, if you go these more complicated routes, you have to buy one or two extra sets of interconnects and if you want to get into upgrading power cables eventually, up to three new power cords. If you buy one of the integrateds that can handle two sets of speakers, you save a bundle on wires.
Some ideas anyway. Again, good luck.