Well, this fell through the cracks and I just forgot about it. I'm doing an unrelated fix, so might as well give this another crack.
The reason I didn't want to consider Heavy Oil energy capacity before was due to how complex oil processing is. However from what I can tell, it's more efficient to produce Solid Fuel Heavy Oil Cracking -> Solid Fuel than from Heavy Oil -> Solid Fuel directly. The latter is 20 Heavy Oil -> 1 Solid Fuel, or 40 Heavy Oil -> 2 Solid Fuel, at a cost of 840KJ and a gain of 24MJ. That's a gain of 579KJ per unit of Heavy Oil. The former is 40 Heavy Oil -> 30 Light Oil -> 3 Petroleum at a cost of 1.68MJ and a gain of 36MJ. That's a gain of 858KJ per unit of Heavy Oil. There's no gain in volume from Light Oil Cracking -> Solid Fuel, so that's the cost we're trying to beat.
Just for the sake of completeness since we'll need it, though: 20 Petroleum -> 1 Solid Fuel costs 420KJ and gains 12MJ. That's a gain of 579KJ per unit of Petroleum. 10 Light Oil -> 1 Solid Fuel costs 420KJ and gains 12MJ. That's a gain of 1.158MJ per unit of Light Oil. That should give us enough data to calculate with.
Let's use Advanced Oil Processing for Solid Fuel. It gives us 25 Heavy Oil, 45 Light Oil, 55 Petroleum. So that's 25 Heavy Oil + 52.11MJ's worth of Light Oil and another 31.845MJ's worth of Petroleum, for a total of 81.855MJ when Refinery cost is accounted for. Without Biodome Industries, the Heavy Oil would be worth an additional 21.45MJ's worth of Solid Fuel. So Biodome Industries needs to be competitive with that.
OK, so what's the cost of Wood Gas? If we go from scratch, then that's a 10 craft in the Biodome which consumes 93KW and produces 10 wood worth a total of 20MJ. That costs 930KJ, which gives us 1.907MJ per piece of Wood obtained that way. Wood Gassification produces 7 Coal and 100 Wood Gas over 5 seconds. That's a crafting cost of 1.05MJ and a gain of 28MJ's worth of energy in coal. In other words, each unit of Wood Gas already nets us a gain of 269.5KJ. It's important to note that this energy gain is theoretical due to side products, not an intrinsic value of the Wood Gas itself. Currently, it's a waste product the player needs to get rid of, because Solid Fuel from Wood Gas is only slightly less bad than Heavy Oil -> Wood Gas, while it needs to compete with Heavy Oil Cracking -> Wood Gas.
So... Heavy Oil -> Solid Fuel is a gain of 579KJ per unit of Heavy Oil. Heavy Oil Cracking -> Solid Fuel is a gain of 858KJ per unit of Heavy Oil. Currently, Solid Fuel from Wood Gas is a 2s craft time at a cost of 20 Wood Gas and 20 Heavy Oil. I'm reticent to consider the energy gained from including Wood Gas because it makes no sense to me intuitively. If Wood Gassification didn't produce Wood Gas at all, then nothing about Solid Fuel production would change, so I don't accept that incorporating a "waste product" somehow increases the productivity of a recipe. Players might as well get themselves a Flare Stack mod and vent the Wood Gas, then just go with the Light Oil Cracking they're already doing at their refineries anyway.
With that said, we'll consider Wood Gas to be "free" - neither a net negative nor a net positive. It's a thing we're getting from an energy-positive process of making charcoal. As such, we need the Solid Fuel from Wood Gas recipe to exceed the efficiency of Heavy Oil Cracking -> Solid fuel. Let's say we up the Wood Gas cost quite a bit, to say 40, but drop the Heavy Oil cost down to 10. 10 Heavy Oil per 1 Solid Fuel costs 420KJ to make, gives us 12MJ back, or a total of 1.158MJ per unit of Heavy Oil. That's a significant increase over the energy gain of 858KJ per unit of Heavy Oil from Heavy Oil Cracking -> Solid Fuel. It might be a bit too significant, but I think I'm happy with it, honestly.
Long story short, expect the Solid Fuel from Wood Gas recipe to change into "40 Wood Gas + 10 Heavy Oil" in this coming patch.