Will I Experience Issues At Immigration Attempting To Stay With My Girlfriend For 85 Days On VWP?

Regardless of how much trouble you will experience during the interview, there is a simple action that would make your journey 100% painless. Instead of flying directly from the UK to the US, make sure you fly through the CBP preclearance facilities in Ireland. That way you can simply walk away and go back home without much extra expenses if you're refused entry at the virtual US border. Likewise the US immigration agents won't detain you and you won't have to wait for your flight home in a miserable detention facility.

You can also do the same if you fly through Canada, however it will be a lot more expensive to get a flight back if you're rejected.

How likely is it that I will be turned away and not allowed to enter the US?

Highly likely!. Especially given that:

The plan is to quit my job before leaving

So:

She is coming to the UK to visit me this summer for 1 month

Bring all documentation proving this to the US border, so they see it "goes both ways" so to speak.

Also, what would happen if I was to be turned away at the border?

You cannot enter visa-free ever again unless becoming a permanent resident, and will have a black mark on your record making it harder to get a visa, which is also harder in general than entering visa-free, given the much closer scrutiny you're subject to.

I believe in telling the whole truth at the border and will not take the advice of describing her as a 'friend'

It would not be credible in the slightest for an 85-day stay to be honest, so you're doing the correct Thing.

During this time, we will be staying with her parents at their family home and I should have between £4,000-5,000 saved

Save all bank statements starting from now, and get a letter of Invitation from your girlfriend's parents stating their relationship to you, as well as the duration and motive of your stay.

In general:

Attach every single piece of documentation proving any and all ties you have to the UK, put them in an A4 keeper, and be prepared to present them, along with the return ticket confirmation, on request.

Also I strongly recommend you to use an APC kiosk if available at the airport where you clear immigration. It will do the bulk of biometric and background checks for you, leading the officer afterwards to ask significantly fewer questions (according to anecdotal evidence)

ALSO:

Call the CBP and ask for their advice! While a lot of people will merely suggest an immigration solicitor, the fact is it is the CBP that decides whether you get in or not. They can be reached on +1-202-325-8000 Mon-Fri 2PM-9PM UK time, and you can ask the agent to connect you to a supervisor, given the complexity of this matter, which you must explain in perfect detail.

If they tell you "we can't tell because it depends on each case" (although they have usually been helpful to me) explain that you cannot afford slipping up because you didn't attach the proper evidence, and that you need help preparing yourself.

FINALLY:

Even once inside the US, you're never 100% "safe". At least within 100 miles of the border, the CBP conducts internal immigration spot checks on roads as well as public transport. In the worst case (although it rarely happens so don't overthink it), they could ask you the same questions all over again and conclude that you lied/are lying about the motive/duration of your stay, and should not have been admitted in the first place. In that unlikely event, you would be put into removal proceedings, and as a visa-free visitor, you have no right to an immigration judge.

I agree with Crazydre's answer, assuming you are going with the 85 day plan.

With a few exceptions, such as college students spending the summer traveling but required to be back by September for Fall classes, people with strong ties to their home cannot be away from it for 85 days. You are planning to give up your job, and have not mentioned anything else that would make you go home. Your plan for temporary Christmas employment could be carried out almost as easily in the US as a visa overstay as by going home.

You should at least consider an alternative that will get you less time with your girlfriend than this one would if it works, but has a better chance of working.

Keep your life in the UK in full operation unless and until you get a fiance visa. Take as much vacation and unpaid leave as your employer will allow, and still write a letter saying you are an employee in good standing and expected to return to work on date X. Keep your living arrangements. A much shorter visit will be inherently less suspicious, because it is more consistent with intent to return home.

Invite your girlfriend to visit you next, and meanwhile keep in touch by Skype etc. You will be building a history of saying what you are going to do, and doing what you said, that will strengthen future entry and visa applications.