Pre-purchase check (RACV or mechanic) - worth it?

[Keladry]

I'm buying a 2003 Fairmont for my first car, done 209,000 kms, had an LPG system installed in 2007 from LPGas Lilydale (actually I forgot to ask/not sure how to tell from looking so will check the documentation but I assume it's a mixer type). Visually it looks good - paintwork all seems smooth, I couldn't find any rust, interior is clean, electronics all work and I admit I don't know much about looking under hoods but the oil was clean. Tyres (including the spare) seemed ok but again I'm not sure how to check exactly how much tread there should be.

When I test drove it, it felt good - no shuddering when braking (gently or harder), tried turning with steering wheel as far as it would turn and the steering seemed tight and responsive. It sounded smooth when idling at the lights. I didn't notice any weird gear changes.

The owner warned me that he once had the engine stall when switching over to gas when rolling down a hill, and that the lpg mechanic advised him to only switch over going downhill if he was accelerating. When I tried switching a couple of times there was a slight noticeable 'something' on the change but otherwise the car did not act differently.

The owner has a nearly complete service history (a couple missing) from Etheridge Ford and a separate service history for the LPG (and is getting this serviced before I buy it). He is also getting a RWC.

Should I get the RACV or an independent mechanic to check the car before handing over my money ($6500)? Is it worth it, seeing as there's a good service history and they only examine parts visually? I accept that having done over 200,000 there are going to be parts that need replacing soon/eventually but can a mechanic tell this just by looking? I've heard about problems with the transmission in the BAs and will get an external cooler installed once I buy it anyway.