The issue here is that changes to one thing affect the other, so you want to have something like perhaps a mock up in cardboard of the enclosure that isn’t a huge cost or amount of work that you can change easily and cheaply (enclosures are typically expensive if you make a mistake) along with a cardboard mock up. print a copy of one side of the pcb layout (to get the position of the mounting holes), tape it to a piece of cardboard or a thin sheet of rigid styrofoam and poke the components in to the pads on the paper layout to mount the components. That gives you an easy (and changeable) version of your pcb and verifies that the components will actually fit on the board in real life (both useful things). You will likely have to iterate around this loop (enclosure mechanics, board layout) several times to get a working design. For instance its possible that you will do an enclosure and a pcb layout then discover that there isn’t enough room on the pcb to route the traces, meaning you need to move components which affects the enclosure design. It is much better to get it right with a cheap mock up in cardboard than cut an expensive board on ly to discover it doesn’t work and have to redo it. I’d be inclined to start with the enclosure mock up then see if you can place the components and route the pcb to match that design (if not you need to change the enclosure design).
That was a potentially fatal error. If I hadn’t remembered to look for a source of +5V (because Fritzing will happily let me add VCC tags in schematic without a source of power to drive them) you would have routed the board and it would show routing complete but not actually work, because it didn’t have a connection to +5V anywhere. You should verify every wire on your physical breadboard is also in the Fritzing breadboard view as I expect those two wires are on your physical breadboard (because it works) but not in Fritzing (which is a problem). Note that you need to make this change in all your sketches as well so if you end up using one of the other ones you don’t hit the same error and not catch it before you buy a board.
Have you connected the neo pixels to your breadboard set up and run them? It is possible (but I think unlikely, although I’ve never actually used neo pixels) that they take less current than I expect. I do know from articles from people using them they have ugly power draw issues due to how they work. The issue is the 5V connection from the mega can only supply a limited amount of current (I can’t see a spec for 5V but the 3.3V is limited to 50ma, to be powered from USB the 5V line has to be less than .5 A and I expect the output pin can only supply 50 ma as well). I expect the neopixels will take a lot more current than that (possibly several amps) but you may have few enough of them that they won’t need that much. From the 2 1000uf capacitors, someone expected the neo pixels to draw a large amount of current I think (whether they are correct or not is another matter 
.)You would need to check the specs for the neo pixels you use to see what their maximum current draw is (and I would size the power supply to the maximum current draw!). If the mega can’t supply the 5V to the neo pixels (which I think is likely) then you need to be able to supply the 5V for the neo pixels some other way. A 12V multi amp (sized to match the neo pixel draw) wall wart will supply the 7 to 12V the mega needs and one of the ebay buck power modules (there are fritzing parts for several in parts submit, but I don’t think in core) will reduce the 12V from the wall wart down to the regulated 5V the neo pixels need. From your point of view that means you probably need to add a coax power jack to connect to the wall wart in Fritzing, which is the source of 12V. A 1n4004 diode and a 100UF capacitor then connect 12V to the Vin pin on the mega (this should be able to power the mega from what I see in the mega reference schematic and the diode and cap isolate the mega from 12V voltage fluctuations caused by the neo pixels). This forum thread:
has pointers to 2 such converters (limited to 2 Amp output I think) that have fritzing parts and are available on ebay and others. You would need to verify that 2A is enough current to run the neo pixels first (and find a higher current model if not). Now the 12V input from the coax jack goes to the input side of the buck module, and the output side (which you need to adjust to output 5V before connecting the neo pixels!) provide the +5V to the neo pixels (with probably just 1 1000uf capacitor). Assuming you can use one of these converters a 12V 1A wall wart should be fine (cheap and common) as that would provide about 3A at 5V via the buck module. You should modify both your physical breadboard and the Fritzing sketch to add these things and then test the physical breadboard to make sure everything still works correctly. Then you should be ready to do the component layout in pcb (as there are now a few more parts) and see how you can make the enclosure once you have everything you will finally need connected up.
Peter