i used to be a stats major, and let me tell you something that may be comforting:
tho each pack of buying amiibo cards is an independent attempt to draw the cards you want from the last, there is still a 5/80 or something chance of drawing them; 5/80 = 6%, which is higher than an "alpha" that a lot of statisticians use of 5% to decide whether or not an outcome is statistically significant (in this case, without considering any outside factors, there is a statistically significant chance that you will pull at least one card that you like, even though it is low)
there is a 75/80 chance (94%) that you won't get a card you like on the first pack, but if you continue to buy them (or buy multiples), that chance decreases by a factor of itself (this only works if each draw is independent of the last, which it is).
for example, if i buy 5 packs, i can multiply that 94% by itself 4 other times (5 times total):
.94*.94*.94*.94*.94 = only a 73% chance of not getting the cards you want (or a 27% chance of getting a card that you did want)
TO CONCLUDE, i think ur best bet is buying packs lol; less money than the cards you want if statistics favor you, more potential villagers to choose from regardless, don't have to delete your town, don't have to shell out for another system
edit: on the other side of things, if you do a 2017 new year's reset (without following the "rules" of the new year challenges), i can let you bring some of ur old stuff that u want to keep to my town until you have a new town and then you can get it with your new mayor :^) just pm me and we'll arrange something