I recently purchased a multi-grip pull-up bar that requires stud placements that equate to 48". https://xmarkfitness.com/products/wall-mounted-pull-up-bar
When finding the stud locations, it was then that I noticed that my house doesn't have them placed at the appropriate measurements. They're at 18" OC. The hole next to the yellow bar allowed me to stick in my phone in order to verify the stud next to it. The following studs were found with a stud finder. 
Red bars are where studs are located at.
Yellow is wiring for a light behind the door.
How am I supposed to proceed next? I was thinking of making a board out of 2x6s and attaching them to the studs with a bunch of lagscrews.
Blue bars represent an idea as to where I would attach these boards.
Does this sound like a decent idea?
Is this safe?
Any idea on the length of the lagscrew I'd need for this? The wall is 1.25" thick.
Any other suggestion if this isn't viable?

