I was watching that one on eBay to see what it went for. Nice snag!
The bergara should fit in fine, as long as it doesn’t have an oversized recoil lug (which I don’t think it does). Where you might see issues is the trigger, depending on what you decide to use. Early Timney sometimes had to have a little relief work done, I don’t know of the stock bergara triggers. Will be easy to tell when you get it though.
The long action single stack mags will work fine (and are what you need for the chassis anyways). The AW reference is for the double stack short action AW mags - they require some work in a stock Remington action to feed correctly since they’re staggered vs single feed (think AR mag + feed ramps vs single stack AICS mags).
I like Remington actions, especially ones that have gone off to a smith. If it were me that’s what I’d drop in and have it pretty close to the mk13 look. Nothing wrong with the Bergara though.