I have never tried this but its worth considering.
When bulding new boats vacuum infusion are becoming more popular it is a effective and inexpensive way to distrubute resin in a laminate.
You could do it the same way.
Drill some injection holes at the centre of the damaged area and holes for vacuum at the edges.
Apart from epoxy (or polyester) you will need plastic film, tape , hoses and a vacuum pump. If you google "vacuum infusion" you will get lots of hits.
The vacuum pump is the most expensive equipment. I have read som articles on using an old compressor from a fridge for this purpose. Or maybe you could by or rent one?
Just an idea
A boat repair shop close to my waters have recently started to look at vacuum infusion for repairjobs. (Don't know if they would use it to solve delamination thoug)