Screwfix have a wide selection of various lengths vine eyes so worth a look as to stocked sizes and go from there.
...the problem is that the Vine-eye screws come in different size 'gauges', whereas rawl plug sizes are in mm. Hence the confusion. eg. The max size rawl plug I have seen is 10mm. What is the best 'gauge' size vine-eye screw to correspond with that?
For 12 gauge the brown wall plug would fit. Wall plugs come in screw gauge sizes, yellow red, brown, grey, blue etc Look for wall plug sizes on internet but from memory 10mm is a blue plug.
or https://www.screwfix.com/p/rawlplug-rawlbolt-eye-shield-anchors-m8-x-87mm-5-pack/95131 and larger.