You are punished for changing the game time (no matter how much, it seems), but not the system time. Here's what happens:
If you change the time on your 3DS system, Animal Crossing seems to simply think that's the time it is now. Trees grow, events change, the only "bad" things that happen would have happened with the flow of time. Even going back in time via this method seems to work okay, even when going to a day previously played.
If you change the game time, using the option at the main menu of Animal Crossing, you will randomly trip for a while after changing the clock. The duration of tripping seems to last longer than the current play session, possibly the full day? But it eventually goes away. If, however, you were to change the game time this way before every play session you would trip randomly every single session, which is highly frustrating.
Also note that going backwards in time will spoil any turnips you had, since the game knows you went backwards, while it doesn't know you went forwards if you go by the system clock.
tl;dr: Change your 3DS's system time to time travel, do not mess with the in-game clock regularly or will will randomly trip.
Does that mean that I shouldn't give my highest scoring bugs first?
Yes. If you want to get as many items as you can get you should start off weak.
I'm also concerned that if I give lower quality bugs that I'll get lower quality furniture, or will Nat always give you a piece of the Bug set regardless?
How it works is until you meet a certain point level (it was 80 points for me) you will get normal furniture from him every time you break the record. After you break that level of 80? points, each new record after that (including the first) will yield another bug furniture.
So I'm not even entirely sure I can direct the outcome the way I want to but I'd like to try. What should I do to guarantee the most pieces of Bug furniture?
Bugs are graded by three things: rarity (easiest to "manipulate" but you have to find the right bugs), relative length (the game tells you this right when you catch the bug, if you can sort your bugs of the same type by length) and luster/color (this is random and there is no indication of luster until you give it to nat). To maximize the bug items you get, start with not-so-rare bugs and work your way to the rarer ones, working in order of size when you have a bunch of the same bug.
Rarity can roughly be measured by how often you see a bug around. Common butterflies are super common, tiger butterflies are uncommon, emperor butterflies are sort of rare, Raja B butterflies are quite rare, as an example.
Note that the bug off is held monthly, and you probably won't get all bug items in one month. Personally I only managed to get two (I could have gotten more though).
Also not that at the end you'll get a ribbon based on performance. You get a ribbon based on placement, not on how many bugs/furniture you've gotten. A single, high scoring bug will get you a gold ribbon.
Best Answer
In my experience, sneaking up on bugs in New Leaf works better when you:
As I mentioned in the list above, a good place to practice your sneaking is the tropical island. My advice for the island is to strip your island of most (if not all) normal trees, and all flowers, leaving only palm trees. This is because normal trees and flowers will spawn bugs that are worth less than bugs that will spawn on palm trees. It will also spawn bugs that don't require sneaking to catch, which would be impractical for this exercise.
For easier bug catching, I also recommend that you cut down all palm trees that aren't on the left, right, and back of your island with respect to the camera. Something like this:
Legend:
Bugs that spawn on palm trees all have a very high sell-value, and you can practice sneaking on them without damaging your village. Setting your island up in this manner will ensure that only palm tree bugs, wharf roaches, and hermit crabs will spawn on your island.