Sorry to hear about your delivery trip problems. I hope they got sorted out okay and you're happy with your boat.
I bought an 1982 Carver 3007 in June. I did a two hour sea trial. I had a marine survey conducted by a surveyor recommended by a yacht broker friend who lived and worked in the city where I was buying the boat, and with whom I'd worked for several years. I also had the engines inspected by a marine mechanic, also recommended by the same broker friend. Lastly, I had samples of the engine oil and transmission fluid analysed by a lab.
The mechanic ran the engines while at the dock. Crusader 220 hp, FWC. He checked the fresh water cooling system and the raw water system and found that the raw water pumps needed to be serviced with new impellers and replacement of worn components, and that the coolant in the FW system needed replacing. He noticed that the sea strainers were not bonded. He recommended replacement of the transmission coolers due to their age. I learned that the transmission oil had likely never been changed. Of great importance to me was the condition of the exhaust manifolds and risers, and the heat exchangers. The mechanic removed one riser to inspect it, and he removed the end caps on the heat exchangers to inspect and "rod them out". The mechanic checked the packing glands as well as the charging system. He also checked the ignition and fuel systems, batteries and battery cables, controls and control cables, instruments and indicators, making a number of recommendations for each.
I paid $400 for the mechanical inspection. I received a very thorough multi-page written report with recommendations for each system inspected. I had $1,800 of mechnical work done to the boat before I took delivery. Delivery for me was a two day voyage during which the only problem I noticed was that the port engine was running hotter than the starboard engine. I discussed this with the mechanic after the trip and he made a number of suggestions, and advised that the temperature difference wouldn't have shown up when the engines were run under 'no load' conditions while at the dock.
The oil samples were of limited use as they were essentially a snapshot at one particular point in time, whereas a database of information acquired from regular sampling done at regular intervals before and after changes in use, repairs, alterations, etc is needed to provide a complete analysis. As one poster to this forum suggested to me when I inquired about fluid analysis, if you don't have fluid samples analysed you won't learn anything; if you do, you might learn something you didn't know.
I definitely recommend having a separate mechanical inspection done in addition to the marine survey. You'll learn a lot from the inspection. The only thing I would do differently is to try to have the mechanic aboard during a sea trial so he can inspect the engine while under load. The pre-delivery service work I had done I saw as a pay-now-or-pay-later thing.