You are correct in assuming that your compressor ratings are inflated...most manufacturer's of smaller compressor do embellish not only the CFM output but, if your compressor is plugged into a 110 circuit...I highly doubt your getting the advertised 5 HP out of your electric motor. If in fact you are running a 110 Volt outlet to run your motor, your HP rating would be closer to 2 HP.
You have a 15 gallon holding tank, your compressor is rated at 6 CFM at 90 PSI, which means that at 30 or 40 PSI, your maximum CFM output would be (and this is a guess as I don't know other specifications of your compressor) about 9 CFM...that is maximum. Your average spray gun uses about 10 to 12 CFM...so to answer your question with a question, how small a surface area can you break your engine bay up into to prime? If you broke it up into 6 pieces, rad support, driver's side inner fender, driver's side wheel well, firewall, passenger's side inner fender and passenger side inner wheel well...you would still be pushing your compressors, capability to prime your project in sections. The compressor would be running constantly and as you mentioned, it would create moisture from the heat build up...even on smaller areas like your inner wheel wells. You can add a oil/water separator...it would help...for a little while but, as you continue to prime, water will get through your gun and onto your painted surface. It would help to let the compressor cool down when your holding tank is depleted and your compressor has run for a while...but if you plan on priming all sections of your engine bay in one day and not get any moisture in your primer...you will in all likelihood be there all day and still be at risk of getting moisture in your primer.
One suggestion I could make to make life easier on you, (not so much for your compressor) would be to get a larger holding tank...you have 15 gallons now, if you where to add another 45 gallons, you may be able to get through priming 1 of 6 sections without your compressor being able to spit water out through your gun...band aid on a broken leg scenario...but other than accessing a larger compressor, that's all I could with clear conscience recommend. In fact, if you really like your car and you want to do a good job without a probability of having moisture in your primer...get a compressor that puts out more CFM, has a larger holding capacity....and if at all possible (don't know if you have 230 connection your garage but) an electric drive motor that is truer to the rated 5 HP you have now.
Sorry to be the bearer of not so great news but, you asked the questions and I look at it as though I'm an honest salesperson at a compressor store...I would recommend a larger compressor at the time you purchased it with what you want to use it for now.
Hope this helps.