It turns out that all that worry (I wrote about it here) about how to procure a visa for India was unnecessary.
Before we left on a family trip a month ago, I researched and debated using a fairly new system, called Tourist Visa on Arrival, rather than the standard method of sending your passports to a third party and paying them to process and deliver your papers to the Indian consulate. This third-party process was quite expensive (for the four of us it would have cost about the same as buying another plane ticket) and time-consuming, and I had heard horror stories from travelers about not getting their papers back in time.
We went with the simpler, cheaper ($60 per visa) online process, which involves uploading photos and passport images at the Indian government's TVoA website, and then printing out the e-mail that says your visa has been granted. This becomes your visa, which we showed to the agent at MSP when we checked in.
When we arrived in Delhi at 2 in the morning with our two young children, we simply got in a separate line, clearly marked Tourist Visa on Arrival. The agent took our papers, took our fingerprints, and then stamped the visa into our passports. The process was somewhat slow – each person took about 10-15 minutes – but otherwise efficient and simple.
I would highly recommend this route if your travel fits the visa's guidelines: you're staying for less than 30 days, you only need a single entry, you're visiting as a tourist, and you have a return ticket.