Current Engineer at a Portfolio Company in the Oil and Gas Industry looking to get into PE

I'm an A&D/Reservoir Engineer at a PE backed shop, and have been thinking about jumping into the finance world. I joined this gig straight from school and it's been about two years. I'm lucky to have been given lots of responsibility right off the bat in the A&D side of things where I've successfully closed ~500MM in A&D deals, while also working on the engineering modeling and econ modeling side of things. Recently, I've been thinking about my next few moves and have been lured into ending up in PE. I'm aware that engineers are generally not the target for an associate gig at PE funds, but given my background in A&D, would I have any sort of chance in the Oil/Gas Energy Fund as an associate?

Obviously, doing an MBA, followed by 2 yrs of IB, and then recruiting to PE would make the most sense. But it'd also mean that I would have to wait another 3-4 years max to get into PE. From the experience of all WSO PE guys, what have y'all seen out there from engineers that you might've crossed paths with either during recruiting/meetings? Would also appreciate any advice on what I should ideally be doing so I end up in the PE path within the next year or two, max. Thanks!