So, in case that mini dungeon event does come back...

I take it from the answers so far that pets aren't necessary?

Also, is this taking into account my limited funding? cause i'm pretty sure I probably can't share 2x drop cards with other characters on my account, and I may not even be able to afford buying extra tries either. I've got no idea what to do there and it's probably hopeless to think that I'd be able to get even the least that I want to go for.

Pets with Item Bags would be helpful, but you could also just pick the crystals up yourself and save some NX. I'm fairly certain, if given the same time to collect crystals as last time, that you could at least be able to get the chair, if not a necomimi also.