HELP! I bought a mess?

This is my first post with the forum. I have a moderate amount of mechanical experience. Please forgive the length but I want to give the most information I can upfront. I recently purchased a 1967 Barracuda convertible from my uncle who owned it for the last 15 years. He was not very mechanically inclined and just enjoyed cruising it. The engine combination has thus survived the test of time and not chewed itself up but I am not sure what to do with it. It has the original '67 273 short block in it as evidenced by the casting number and the date stamped on the front of the block under the driver's head. He told me the guy who had it before him had put 340 heads and an Ede LD340 intake on it. I am finding on here that that combo should have caused a lot of problems with the 2.02 intake valves making contact with the deck unless the deck was clearanced. I have not pulled the heads yet. I have pulled the valve covers and the casting number of the heads is 341895. Also cast into the passenger head only is the number 360. Larger than all of the other cast numbers. I am assuming then that these heads are the 70-72 360 heads that used the same casting number as the 340 heads. They used the 1.88/1.60 valve sizes. Is this maybe why the heads seem to work with the 273 without interference? Would this be a good assumption? I have the original (confirmed by the casting number) 2bbl intake and carb and a set of 4027593 casting heads claimed to be the original 273 heads. Rockers are missing. Claimed to be on the "340" heads. Casting looks up as 77-83 318 heads. "340" heads have what appears to be the 273 adjustable rockers on them. Goal for the car is a nice weekend cruiser for the wife to drive to the car shows and enjoy and one that I can step on occasionally and have fun with when I drive it. I have my '69 Roadrunner for going out and thrashing.

So the questions:
Are these likely 360 heads?
Did the 70-72 360 heads have adjustable or stamped steel rockers originally?
Assuming this is a '67 273 with 70-72 360 heads (1.88/1.60 valves) and a LD340 Ede intake, is this a combination that is worth rebuilding and retaining?
I have a 2001 360 Magnum core that I am considering trading in for a new long block and doing a Magnum conversion and parting out the mixed engine combo I have. Thoughts on this route?