Wheat Wine Barrel suggestions: Bourbon! The sweetness of bourbon is just going to supplement this already sweet, malty beer and the smokiness and woodiness from the char should add some depth and complimentary flavors. Another great option would be a red wine barrel. A semi-sweet red rather than a sweet dessert wine would be preferable as it wouldn’t over-power or add too much astringency and would also let the oakiness through. This would obviously present some fun branding opportunities; especially if we stayed with the name House Red.
We increased our Flaked Wheat contribution to 8% and reduced the Red Wheat and Golden accordingly. This should add a bit more body to the beer to compensate for the body thinning out while it's doing its thing in the barrel.
Next, we would remove both the aroma and whirlpool Lemon Drop additions to avoid off-flavors related to hop degradation in the barrel. Half of the batch would simply go into the barrels listed above for a more traditional barrel-aged product while we would rack the other half back into a fermenter for a dry-hopping regiment. Ideally, would have done this before and racked into a bunch of separate, small carboys to experiment with which hop would work best. Some options might be Lemondrop for a more lemony, citrusy, and piney effect, Nelson Sauvin to stay with the wine theme as it has a lot of white wine characteristics, or Legacy which would provide notes of black currant and a spiciness that could work well with either barrel.
Our US-05 yeast remains a solid choice for barrel-aging as it will do an excellent job of flocculating out fully with a long, slow fermentation schedule; especially if we crash it on the low side of 50F or so for a few days before transferring to barrels. It's clean fermentation profile also means we won't need to worry about any phenolics falling off through the barrel-aging process.
All-in-all, our gravities and mash schedule are already pretty ideal for a barrel-aged product; we are mashing high to maintain body and our finishing gravity of 1.022 should help the beer fare well in terms of reducing the chances of a "hot", overly alcoholic product.