I'm installing 3/4 by 2 1/4 solid and am curious about base shoe widths. I really can't remove the base mouldings and a lot of the job is up by the kitchen cabinets base plates. I have read here that base show is 7/16 wide. How do I cover the required 3/4" gap then? Do they make a wider base shoe or do I need to go to quarter round? I prefer the look of base show and always assumed it was 3/4". I'm kind of surprised it's not.

You can undercut the baseboard and or drywall up 1" from the floor to allow for a greater expansion space behind the base shoe.

You will appreciate the refined look of the thinner base shoe IMHO.

I suppose I can do that, but what about where it comes up against my kitchen cabinets? I will be going around an island counter and then there are cabinets on both sides. Since these are narrow aisles, do you think a little bit less of a gap would be a problem here? The way the rest of the rooms and hall lay out, undercutting would not be an issue.

Every professional contractor will fudge some standards from time to time. You might find that you would not have an issue fudging in the narrower parts of the kitchen. Though, undercutting the front of cabinets is usually not a problem either. Cabinets are put together in sections that are supported with 4 sides touching the floor. Cutting the front off still leaves 3 sides of each cabinet section that will support the counter top and cabinet.

Of course as you look at your layout you will need to figure out what not to cut. Outside corner cabinets can be tricky sometimes. Since undercutting both outside edges of the cabinet leave only two supported sides of that cabinet section.

Sometimes this corner is the space for the dishwasher. Where a backer support could be installed to support the cabinet. With some planning and common sense you will be fine.