The counterop weighs less than 300 lbs. The cabinets probably weigh less than 100 lbs. This is about 400lbs spread over a floor area of almost fifteen square feet. this is less than 30 lbs per square foot.
An adult standing still is about 150 lbs on one square foot.
You should have no problem with the load regardless of the placement with regard to the joists.
Protecting the Cable
National Electrical Code 2014
Article 300 Wiring Methods
I. General Requirements
300.4 Protection Against Physical Damage.
(F) Cables and Raceways Installed in Shallow Grooves. Cable- or raceway-type wiring methods installed in a groove, to be covered by wallboard, siding, paneling, carpeting, or similar finish, shall be protected by 1.6 mm (1/16 in.) thick steel plate, sleeve, or equivalent or by not less than 32-mm (11/4-in.) free space for the full length of the groove in which the cable or raceway is installed.
Exception No. 1: Steel plates, sleeves, or the equivalent shall not be required to protect rigid metal conduit, intermediate metal conduit, rigid nonmetallic conduit, or electrical metallic tubing.
So you have a couple options.
Free Space
Run the groove deep enough, so that there's 1 1/4" of free space in front of the cable.
Steel Protection
Protect the cable using a 1/16" steel plate, or sleeve. Or install the cable in rigid metal conduit, intermediate metal conduit, rigid nonmetallic conduit, or electrical metallic tubing.
Dividing the Circuits
National Electrical Code 2014
Article 210 Branch Circuits
I. General Provisions
210.11 Branch Circuits Required.
(C) Dwelling Units.
(1) Small-Appliance Branch Circuits. In addition to the number of branch circuits required by other parts of this section, two or more 20-ampere small-appliance branch circuits shall be provided for all receptacle outlets specified by 210.52(B).
III. Required Outlets
210.52 Dwelling Unit Receptacle Outlets.
(B) Small Appliances.
(1) Receptacle Outlets Served. In the kitchen, pantry, breakfast room, dining room, or similar area of a dwelling unit, the two or more 20-ampere small-appliance branch circuits required by 210.11(C)(1) shall serve all wall and floor receptacle outlets covered by 210.52(A), all countertop outlets covered by 210.52(C), and receptacle outlets for refrigeration equipment.
Exception No. 2: The receptacle outlet for refrigeration equipment shall be permitted to be supplied from an individual branch circuit rated 15 amperes or greater.
(2) No Other Outlets. The two or more small-appliance branch circuits specified in 210.52(B)(1) shall have no other outlets.
Exception No. 2: Receptacles installed to provide power for supplemental equipment and lighting on gas-fired ranges, ovens, or counter-mounted cooking units.
So as far as your plan for dividing up the circuits, you're spot on.
Best Answer
Looking at the actual code...
The receptacles supplying the countertop, must be supplied by at least two 20 ampere circuits. However, these two circuits can also supply receptacles in a "pantry, breakfast room, dining room, or similar area of a dwelling unit", as well as "receptacle outlets for refrigeration equipment". One of the more common ways to meet this code, is by splitting the duplex receptacles. One circuit powers the top outlet of the receptacle, while the other powers the bottom outlet. Another option is to supply the countertop receptacles with one circuit, and the refrigerator with a separate circuit.
As for the receptacle in the kitchen, supplied by the living room circuit. While this is likely not a violation. This receptacle does not count towards the two 20 ampere small appliance circuits required in the kitchen.