Sorry for the confusing photos.
The actual countertop can be seen in the top 2 photos, it's on the ground leaning against the sink (the 6" piece you reference was just temporarily there for looks) and it's about 21" deep by 30"+/- wide. Will butcher block need to be mounted to allow for expansion in both dimensions?
The kitchen cabinetry is in sad shape. It may seem as if I'm making a silk purse from a pig's ear, but I'm trying to renovate the kitchen without replacing everything. A better explanation is here with more photos:
OK. The original cabinet was falling apart and the drawers didn't work. I made a new face frame and am making new drawers (on Blumotion sliders vs. original wooden drawer runners). I'll make a cutting board like the original that must have existed, but I never saw, which will be stored in the slot under the top. Two cabinet doors are being stripped and refinished. No toe kick: originally there was a narrow strip of molding on the floor with a raised rabbet at it's back as a stop for the doors (similar in look and profile to a floor saddle/threshold plate ... in fact I have a spare one that the guy who installed new floors in the kitchen stained and finished for me to match the oak flooring, which I'll modify and use). I may at a future date, make two cabinet-wide drawers on slides (either keeping the doors or getting ride of the doors) and in that situation I'd likely retrofit a rail/toe kick at the bottom.
I also added extensions to the sides of the cabinet to make it deeper (so it will hold a larger modern day microwave oven) and lowered the countertop a teeny bit.
Everything is skewed in here (!) which is what's made my first kitchen cabinetry work exceedingly challenging. Not as bad as the Tower of Pisa, but enough to make things challenging. The bottom of the cabinets 13" above the countertop is not level (when I put a microwave on the countertop it's a tight fit to the bottom of the cabinets ... and an angled gap would be glaring and draw the eye). The top of the sink is not level, it tilts forward ... the counter top is less than 1/2" away and its top is about 3/4" below the sink's top ... so if the counter top is level it will not be on the same plane as the sink and where there edges meet will be an angle making everything look crooked. Everything is skewed one way or the other. Actually the stiles on the built-in are the most plumb.
So, what seemed like a straightforward undertaking, i.e. building a new face frame/deeper cabinet/new countertop became an exercise in 3D chess. If I get the cabinet level and plumb it doesn't flow with the rest of the kitchen which is skewed ... it looks off and accentuates how off everything is. So my priority was to adjust things so the eye isn't drawn to glaring imperfections and to ease them so things flow together and the kitchen looks tightly put together (allowances are made for, and are read as 'character' of course in vintage stuff) at the expense of a perfectly level counter top, etc.