Hmmm...a "cross bite" is a very general term. It can range from one tooth being out of alignment - which hardly seems like a major problem - or total misalignment of the upper and lower palates, which obviously should be treated. I don't really understand the "problems" that might occur from a single tooth out of alignment, but I'm not a dentist or orthodontist. I did have a complete misalignment of my upper and lower jaws that was fixed in high school (with thousands of dollars in orthodontics and surgery) but my mom had the same thing, never treated it and it was never an issue - she just has an underbite.
Of course an orthodontist is going to recommend $7K in treatment. I would ask around for a referral to an ortho who one of your friends knows personally and try to get the opinion of someone who might be less motivated to have you buy treatment that may not be totally necessary. Find out specifically what the worst-case scenario is with leaving the wayward tooth where it is and what the minimal treatment is. $7K seems outrageously high to me - even upper and lower braces for one of my older kids for 18-24 months of treatment was lower than that, with an estimate of $5K. The orthos in my area have varied wildly on their recommendations for my older kids but were pretty consistent with my 7-year-old, whose cross bit involves all of his teeth. So...seek at least another opinion.
If it comes back that you still really may need $7K to treat, I would still go with the basement now and put off the orthodontics until you have more money or actually have a problem. We did a partial finish in my basement a couple of years ago for about $3K and it's made a HUGE difference in quality of life in my house. With our basement, we spent about $800 on carpeting (we bought a roll on craigslist and hired someone to install it), painted the concrete walls and the ceiling - pipes, beams, wires and all - with a sprayer that I rented from Home Depot (about $500 for the rental, supplies, primer and paint), and spent about $1000 having more electrical outlets installed as well as overhead lights, and the rest was small stuff like accordion doors, lumber to build a fort, some storage units etc. We have some seating that friends and relatives were getting rid of. The paint, carpeting and lighting totally transformed the space even without installing walls and a ceiling and now the kids have a place to hang out and play that's out of our way and it's heaven! I'm kind of glad that we didn't bother with the walls - those are a huge project, are the biggest expense, and if you have any kind of moisture, that's where you run into problems with mold and having to remove and replace drywall. At least with the carpet, if that gets wet it's relatively easy to rip it out and install a new piece.