If you're looking at FamilyCare with Quinn, then you should also look at CompanyCare from Quinn or Company Plan Plus (Levels 1 or 2) from VHI or biz plan plus from VIVAS/Hibernian.
These plans are primarily sold to the corporate markets, but under open enrolment legislation, none of the insurers can refuse to let you join, nor can they charge you any more than any other member of the scheme (aside from group discounts).
Unfortunately, the HIA comparison document doesn't list these plans, which is a shame because they are very similar to the main plans (but not identical so make sure to check) and they are cheaper.
Regarding the reduction of the 5 year pre-existing (I'm presuming it's the pre-existing), it's very unlikely that you will get this reduced unless you have previous insurance that the Irish insurers recognise. If it's any consolation, 5 years is the market norm, VHI & Hibernian have the same.
As for ease of use, I've had no personal experience using health insurance (and long may that continue!), but I've heard that Quinn are asking alot more questions of doctors and hospitals before paying claims. This may not necessarily be a bad thing though, as it might mean that errors don't slip through the cracks. Haven't heard anything about VHI or Hibernian. Perhaps you could give the patient accounts dept of your local hospital a call to see what they say (but factor in that what's negative for them may not be a negative for you).