The HP isn't totally wasted. You're in their system. Log into Overstock, click on Electronics, then on right-hand side, click on Overstock card. Then click on Apply. Most likely you'll be taking immediately to step 3 and get 7-10 day message. You won't be getting any more letters no matter how many times you try.
Here's the key, in about 90+ days, they will rescan your reports (may do so earlier for other sites, but likely won't change anything in regards to Overstock) and, if your credit profile has improved enough by then, you may get a pre-approval pop-up when adding an item to your cart and checking out. You'll know they've done a rescan by trying to apply - if the regular application appears instead of going to straight to step 3, a pop-up could be in your future.
Credit scores low as 580-600 will get the pop-up (shopping cart trick; SCT), so you're right at the cusp in that regard. However, it's not just scores, but overall credit profile. So take a look at the reasons in the denial letter. If too few revolvers, apply for another, even if it's a secured card like OpenSky (easy to get, and SP). If it's utilization, pay down cards. If it's inquiries, garden for awhile. If it's baddies, try to settle, PFD, and GW what you can.
In short, you're likely very close, wait some time, and you'll likely qualify via SCT.
