Yes, it would help a bit (as long as you don't fill up that extra limit :-) ). A coworker just yesterday said that he called up his credit card company and asked for a higher limit, and it caused his credit score to increase by 20 points.
Unless you plan on paying that card off at the end of the month, there's no way to get around this. You're using 70-80% of your total credit limit if you just have this one credit card. You're going to take a hit. The ideal situation is to use only 10-15% never more than 20% of your total credit, meaning you would need to increase your total credit limit to around $50,000 to stay within that sweet spot.
I don't know how long it takes you to pay back the 7-8k you spend, I'm guessing since this is an annual thing, you're paying it off before the holidays next year, it couldn't hurt to apply for a higher credit limit card that has 0% interest for a couple years and a low to 0 transfer fee (credit unions usually offer these). This will give you some room to breathe while giving you time to pay off the loan interest free. And after you're done paying this off, I'd recommend never putting that much money on a credit card unless you absolutely need to. Even the best rates for credit cards are around 14% interest, which will cost you more paying it off than it would if you just opened a holiday account and put money in it all year (if you're paying the credit card back before the end of the year anyways, then there is absolutely no reason to ever use a credit card like this). If you're letting that 7-8k balance sit on that card longer than a month, that interest is going to add up significantly.
I should edit this to say if you have a moneyback rewards card and charge this much to it and pay it back in the next statement, you could actually save money. If you have $8k sitting in the bank, then I'd say go for it. But like I typed above, if all you have is that card, or you have multiple cards, your total credit line should be about $50k to stay in the sweetspot if you don't want to take a ding. The good thing is, it doesn't take very long for your score to recover if you happen to use that much credit and then pay it off quickly. If you are applying for a big loan and want the best rates, I definitely wouldn't be using that much credit during this time.
Obviously having a higher balance would affect the debt ratio, because you would have a greater ratio of used to unused credit. That's why it is recommended to have a higher limit, so you are using less of the overall available credit!
Totally agree with the latter half of this thread.
If the company's game (and they assuredly will be because, well, credit card companies!), raise the limit. Of course, you know, please don't go crazy (you assuredly won't!).
Oh, and while you're on the phone with them, why not ask for a lower interest rate too? Seriously, it never hurts to ask, and if you've got a good payment history with them, they're surprisingly amenable to such suggestions. The worst thing they tell you is no, and if they do, it'll be a good thing to remember when you pay down the balance on the card and begin to think you can probably open a better card!
Anyways, good luck... let us know how it goes!