Lighter fluid can create long term problems, so I would use it only as a last resort on carpets/upholstery/mattresses. If you encounter a fire later, the lighter fluid can still feed the fire. this is esp not good on mattresses.
Remember that you NEVER use warm water on blood stains - it sets them in.
If you need to create a stream to get into a tough corner, try reusing a saline bottle from contacts. FYI, AOSEPT contact lens solution is peroxide that changes to saline with the presence of the catalyst dohickey. It is awesome on blood stains. Clorox 2 is also pretty much diluted peroxide and colors, scent, etc (put 1 cup of water in a jug, add water to make 32 oz and it will work just like clorox 2 color safe bleach).
Depending on other spills/stains in the room, you might consider treating with something like Kids 'n Pets after the stains are mostly gone. It is an enzyme cleaner that will neutrralize any lingering odor that might attract a pet and give them signals to mark the area. It is the enzyme treatment we have found most effective with pet accidents. I have always found it in Walmart with carpet cleaners (not with pet stuff). I don't think it would remove the blood stains but I haven't ever had to try it on them. Here is a link to the company website:
I hope this isn't too awful a job for you. I am sorry that it is something you have to deal with.
