That heater core repair is going to be a butt-kicker. Someone in another thread quoted that as a $900+ repair. Since the entire dash has to come out, that's not a shock.
Since you are so close to being out of warranty, you might ask the service manager to see if Mitsubishi will throw you a bone and pay for part of the repair. Most manufacturers have some sort of "after warranty assistance" programs for situations like this, but they usually won't tell you about them. It can often be up to the discretion of the dealer if they want to help you out. If you're a good customer (you have your car serviced at that dealership), they will be more inclined to help you out. You might be able to get a deal where you pay for 50% of the repair. It doesn't hurt to ask.
The FAST key is a tough call. Intermittent issues can be a bear for both the customer and the dealer. Technicians generally don't get paid to track down intermittent problems. When a tech sees a problem on a work order and he can't duplicate it, there's not much he can do. Well...he could spend a couple of hours trying different things, but he normally won't get paid well for that time. He will want to grab the next work order to do a job he's going to get paid for.
If you have an intermittent problem, you may have to wait until you can easily duplicate it before taking it in. Some times that's the only way to get someone to fix it. Have you looked at the FAST key diagnostics in the service manual? There might be some thing you can try there.
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View my fuel log 2015 Mirage ES 1.2 manual: 52.2 mpg (US) ... 22.2 km/L ... 4.5 L/100 km ... 62.6 mpg (Imp)