111 Trophy hunter, scope mount needs adjustments

I have a Trophy Hunter 111 LA in 7mm rem Mag. I'm looking for some advice on what works best with this new rifle.
It came with the Weaver 3-9 scope pre mounted and I find the scope is mounted too far forward and too low for proper eye relief and comfort for my old body.
I was thinking I would change the rings to some high rings and change the mount to picatinny one piece base.
Has anyone else done this change or is there a better way to go. In time I will change the scope but for now I will use it with this one.

The egw rail adds some height and would very likely work with mediums.

I have a Precision Reflex on mine but have used the egw and frankly for the money it can't be beat.

Thanks I appreciate the input. Originally when I bought this rifle I was thinking it would have been a good off the shelf hunting rifle. Now I'm finding that it will need some work to get it right for me.

A Weaver #402 extended base will give you the eye relief you need. I bought a Model 11 Trophy Hunter package with the Nikon scope and replaced the factory rings with Weaver Quad Lock rings from Walmart for about $12. You can get them in various heights.