The fact the engine was running poorly after the radiator failed isn't a good sign. The question is, did the radiator fail because the engine got too hot, or did the engine overheat because the radiator sprung a leak?
Anyway, you're going to need a radiator regardless so I'd start with that. After you get the radiator replaced and coolant refilled, I'd give the engine a start and see where you're at. If it's still running rough or spewing smoke out the tail pipe, you either cracked one of both of your heads and blew one or both of the head gaskets.
As a diagnostic tool, I'm not a fan of relying solely on those combustion gas detector kits. With by buddy Sean's rig, we confirmed he had coolant getting into the #3 cylinder using a leak down tester in conjunction with a cooling system pressure tester and the combustion leak detector didn't confirm the issue.
Here's our Radiator Replacement Video which includes installing a trans cooler.
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If you'd like an upgrade over the OEM radiator, Koyorad makes a nice one.
<iframe width="560" height="315" src="https://www.youtube.com/embed/4hS0pdMzyLo?si=_Js60sVXGrZBoxNp" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" allowfullscreen></iframe>
Here's the video of [MENTION=102606]infamousRNR[/MENTION] (Sean) and I made confirming coolant was getting into the #3 cylinder.
<iframe width="560" height="315" src="https://www.youtube.com/embed/nelMt1UCEnU?si=WHytu92U2nX8sQjt" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" allowfullscreen></iframe>
Finally, here's Part 1 of our Head Gasket video series. I unfortunately think you're going to need it.
<iframe width="560" height="315" src="https://www.youtube.com/embed/iSFpwnCuBDk?si=vdCW_8RSVxb25l9W" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" allowfullscreen></iframe>
Good luck! If you need further help, you can contact me on this forum or on my Timmy the Toolman YouTube channel.