Trim a delicata squash vine?

[HudsonValley]

Last year I tried to grow zucchini -- three times -- and lost them for reasons unknown at the first true leaf stage. This year, I started several squash varieties. I lost one plant to vine borers, but have managed to keep two zucchinis, a yellow crookneck, and a delicata squash alive. The zucchini and crookneck are compact, bush-type varieties that are already producing well. The delicata, however, has produced a vine that stretches 12' from end to end, and is threatening to overtake two tomato plants at one end, two eggplants at the other, and the crookneck next door. It's also growing well outside the bed, and has somehow attached itself to the lawn. Can I trim the plant back, or should I just leave it? I've found at least 3 squashes forming, but I'll bet there are others. Will it stop growing soon? Would a trellis (or two) help?

I know, I should be more careful what I wish for... But part of me wants to take an axe to the delicata and spare the imperiled plants!