restore iphone backup, from previous ios (?)

Super bummer incident at the end of a vacation:

All my video shot on Spark, an app which stitches together your shots on the fly.

As I am packing two backpacks, a guitar and a pizza up to my house and unlocking the door, apparently my iphone was still unlocked AND deleted two apps I used the most: Spark and Waze

Frustrating, I'd lose what I'd shot that day, but I had a backup from the previous day, which I'd made as soon as I got a chance to (my laptop didn't travel with me and I had to get back to my relative's house from a plane and then drive 8 hours home yada yada...)

Too exhausted last night, I finally sat down this morning and read a bit on this. Couldn't easily restore from the backup, had an error message, so went ahead with what people suggested and flat restored iphone to factory settings.

Unfortunately this installed iOS 7.1.2

So now it seems that my backup was in 7.1.1 and I can't restore to that (?)

I downloaded the free version of iphone backup extractor, which says that the backup is good to go. I don't want to use that because I don't think it would restore Spark data anyways.

This is really kind of tragic and if anyone knows what I ought to do to get my 12 days of vacation footage back I would be so, so, so grateful.

Thanks!

PS - The truth is that indeed I already have downloaded most of the "Sparks" to my iphoto. So not all is lost. But there was a whole trove of movies from months before and at the early part of the trip that I fear are lost for good.