Well, first off, I'd just mention that our pricing here at Data Medics is only $325/drive, so much cheaper than wherever you were quoted. Pro recovery is definitely your best bet at getting a good result. One more rookie mistake and it's likely to be game over for the data for good.
If you are insistent on DIY recovery, the first thing you'd need to do is get a full sector by sector clone of each drive. I'd recommend you use either ddrescue or HDDSuperClone for this (both run in Linux only). You can read my ddrescue tutorial here: how-to-clone-a-hard-drive-with-bad-sectors-using-ddrescue-t133.html
. At the very least one or more of the drives has bad sectors to have kicked offline. These two programs are the only non-hardware tools that have the capability to handle some bad sectors. If the drives are in worse shape than just bad sectors, then you'll definitely need pro recovery.
Only after getting a full clone of each and every disk should you begin your work in trying to recover the data logically. Since the RAID was recreated, the mdadm RAID metadata was overwritten on the disks. So now, the RAID parameters and logical volume will need to be manually recreated. It can all be done in R-Studio, UFSExplorer or Recovery Explorer, but it's not likely to be any sort of automatic detection case. It'll definitely need some manual figuring out.
If you do successfully get them all cloned onto good disks, perhaps one of us could do the recovery remotely for you at a discounted rate. You'd just have to invest in some $80 software and the necessary disks to clone the data to.