Easy...
Green- it's not that complicated- house wiring is set up for 120/240 single-phase. What you have is 208/125Y. 120/240 is typically home, while commercial and industrial use 3-phase Y and 3-phase delta power.
On a 120/240 single-phase service, you have two HOT leads (L1 and L2) and a neutral, where one of the leads will be at +120v while the other will be -120... they're both alternating, and always 180 degrees out-of-phase.
In a 208/125Y, you have three legs, each 120 degrees out-of-phase. If you measure from any leg to another leg, you'll see 208v. If you measure from any leg to NEUTRAL (the center of the Y), you'll see 125v.
The simple fact, is that most devices you have in your home, work perfectly well in light commercial environments... that's because 200VAC devices are designed for 220vac +/- 10%. That manages both 208 and 240v with no problems. Connect L1 to one busbar, L2 to the other, and cap off L3, connect Neutral to your neutral busbar, and fire it up.
Purists may argue that a single-phase 240v machine won't 'like' the fact that the two legs aren't 180 degrees out of phase, but in reality, the machine doesn't typically 'know'.
I guarantee that this will work, because my ex-USN Kohler 15kva unit feeds my home with two legs and neutral of 208/125Y to an otherwise 120/240 single-phase house.
Re. wiring the 12-wire generator head for 'double delta'... this WILL work, and you'll see a slight improvement in output, however, it might be worth more to simply devote that entire third leg to running critical single-phase loads like sump-pumps, emergency lighting, etc.
As for making protected cross-connection, there are now UL-listed 'generator backfeed interlock kits' available for most popular service panels- they consist of a metal plate that blocks (alternately) the main and GENERATOR FEED breakers, so that it isn't possible to have both on simultaniously. This is dramatically cheaper than a transfer switch, and they work just dandy. You install the interlock kit, then install a suitable double-pole breaker to panel, connect the generator leads to this breaker, and you're good-to-go.