As you have seen, in the price range you are looking, there are many more bad boats than good. You found a promising one in this Hunter27, so keep looking so you have a comparison.
Things to look out for on the H27 include :
rotten compression post at base of mast. If it has it, there will be a very noticeable depression around the mast step, and lots of cracking. Its repairable, but i'd Keep looking, if you see it.
Leaks around deck hardware, mast, and soft spots on deck, particularly where the stays and shrouds attach. The rigging does not have use chain plates, which I don't particularly like, but it's fine worked for 30+ Yrs.
Check the rudder for delam of outer skin. Can indicate interior damage. Its easily repairable but critical.
Check keel bolts, and the stringers for evidence of hard groundings, improper blocking.
Motor: The one cylinder diesel motors are definitely more clunky and loud, but I have soundproofing around mine (repowered by PO with Yanmar 1gm10) and it's manageable. The 2cylinder's are smoother/quieter but you'll be hard pressed to find on on a 27 footer. 10 hp is adequate to hit 6k in flat water, slower in the chop. Still preferable to an Outboard. They are very durable if maintained.
So, you can find good boats in this price range, but as you have seen, it'll take time and you'll see a lot of crappy boats. I looked at tons of Catalinas, C&C's, Hunters, bene's, etc. Good luck in the hunt, take your time, and have fun. The right boat will find you.