83 GLX V6 Vert Auto - Crate vs. Rebuild, HELP!

I've got a 1983 Mustang GLX V6 3.8L Auto Conv. 89K miles. No rust.

I'm 52. I had the same model/specs when I was 16, so you know, I'm reliving that era but with gray hair.

I am aware that the V6 3.8 is a pile of doody... But I like it anyway.

I'm in need of an engine rebuild. I'm not mechanically minded so I'll be hiring this job out but it seems that there's a number of variants I need to consider beforehand. That's where I get lost. Head gaskets, block, all sound very important. But...no clue.

The car starts right up and drives. It then overheats. I had a new radiator put in 100 miles ago. It now doesn't overheat as hot as it did. But still overheats. Fans all work.

Would I drive this car across the country? No.
Would I drive this car 30 miles? No.
Would I drive it to the grocery store? Yes.

I'm in NY state. I'd like to be able to trust this car to drive to my house in FL and leave it for my enjoyment during the winter.

I have two mechanics that I use in my area. One will only remove and replace the engine. The other will rebuild but he's a notorious corner cutter. I need a third that I would trust and how to talk to him, what to ask, that's where I am stumped. Dad's dead. You're all I've got now!

Any advice or tips appreciated.

Thank you very much for your advice and response.

I have looked into crate motors and the price is good...but then I ask Mr. Google and...S&J always comes at the top of my shopping list and then I read their reviews and them not honoring their warranties and I get cold feet that everyone may be like that.

Do we have anyone that has had good experiences and recommendations of who is the high quality companies are vs johnny flybynights?