I recently app'd for 5 cards and got 3. At the same time I paid my util down from around 50% to somewhere between 1-2%. You can see my before and after scores in my sig, but note that the TU scores dropped because my new accounts started reporting, but my lower util was not yet reflected on their report. Although it technically lowered my util with having the extra available credit from the 3 new cards, it still tanked that score to have a high balance on two other cards. On the reports where my payed off accounts were reported, the scores actually went up a little despite the new inqs and the new accounts which totally reaged my profile...
In my non expert opinion, you will probably see your scores come back up once you get your balances paid down. Good luck.