You need to find out if there is even enough head oil to use a resin ball. Teh Fired UP, even going very deep, is not a very mild ball by anyone's standard's.
You might have to try one of the mildest of balls, such as the Neptune, Tropical Storm, Power Groove Dry/R, Lanemasters Hornet, Visionary Blue/Green Centaur (polished) to see if you can use them. They require much less oil than a Fired-Up, but being resin, they still require some oil.
If one of these fails, then Polyester/plastic will be the only answer.
FYI one of these will clear dry-ish heads much cleaner than the Visionary Slate Blue Gargoyle, a pearl urethane. It is a wonderful ball intended for light oil, but it will not go as long as one of the above resins but will have less backend. It is a control ball, but again, I believe one of the above balls are more useful on lanes that are dry but have enough head oil to permit the use of resun or urethane.
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"None are so blind as those who will not see."