Should I apply for a new credit card?

Neoshoegal

I currently have 3 credit cards (American Express, Santander and Virgin). Last year, Virgin upped my APR from 16.9% to 29.9% and then to 34.9%. I called and wrote to them to ask why I got such a high rate but didn't get a reply explaining things properly (I've sent another letter today as I've been reading up on the rate-jacking).
I got the Virgin Card with the 0% deal but when the 0% ended I got that 29.9% rate, I never actually got the 16.9%
I always pay on time, have a DD with them, have a steady income, ... American Express has actually lowered my rate last summer because I am a reliable customer. Virgin just won't budge.
So I've been keeping an eye an my credit rating, all my accounts are in order (as are my husband's account). I even checked my credit score and it's apparantly excellent at 999. The only negative it mentions is:
"You have several credit agreements (excluding mortgages), and the outstanding balance is high". The percentage of my total credit being used is 73% (again according to Credit Expert).
My balance with Virgin is £2835.
Back in May when I received the letter about the rate hike, I tried to apply for another card but was rejected. I could understand that decission as that time, all the credit cards were pretty much maxed out, but now there are significant chunks paid off. Total debt on the other card is about £5000, I know, not great, but I was self-employed until last year, and a lot of business purchases went on a credit card as the bank wouldn't extend my loan even though again I always pay on time and there have never been any issues.
So, should I try to get another card? Possibly one with a low life of the balance rate? Or even just another with an average APR of around 16%, that's less than half what I'm paying now on the Virgin card.
Or would a loan for the amount on the Virgin card be a better idea?

CannyJock

Paying to check your credit score is a waste of money - it doesn't factor in basic things like your income.

If you've not had any searches on your report for a while then no harm in putting in an application.

Barclaycard have a decent LOB deal - full list of LOB cards here on the main stoozing site (sponsored and supported by MSE).

Can you not move all or part of the Virgin balance to your other cards to max them out? Even with a 3% fee, you'll surely still be better off than paying 34.9% interest?

Perversely, once your Virgin card is clear, you can still use it for normal monthly shopping and clear it every month to avoid interest - that'll encourage a promotion to appear in your online customer area. A decent "existing customer offer" might help you move part of the Amex or Santander balances down onto a lower APR for a period of time.

Neoshoegal

About the credit score, I know, but curiosity got the better of me

I don't have anywhere near enough spare on the 2 other cards to shift the debt. However, husband does have a flexible loan with enough space, so I could shift to that that but the APR is 19.9% so still quite high. Then again that's already a whole lot better than the 34.9%!!!

Regarding searches, there have been 2 searches in the past 6 months, both for insurance quotations. Weirdly, one of them was yesterday even though I didn't ask for a quote (I guess it's my current car insurance company as my renewal is up next month). All the other things in the past 12 months were either insurance quotations or unrecorded enquiries from our own bank.