One-way ticket from USA to Germany & Visa issues

I recently was award a Fulbright U.S. scholar grant and will be living in Germany with my family, ideally for 13 months (however my Fulbright grant runs only for 6 months -- but I'm on paid sabbatical from my university for Protected content , so I will be employed and have income).

I'm trying to figure out air travel and visa issues. We want to fly in late July Protected content ideally stay in Germany until August Protected content . And we need to buy plane tickets within the next two weeks, before fares become too expensive. Round-trip air tickets won't work for us, due to the length of our stay. Which seems to leave us with one-way tickets as our only viable option.

Fulbright advises American scholars going to Germany to obtain a visa AFTER arriving in Germany. However, I've been told by several people (not at Fulbright) that we can't buy a one-way ticket without already having a visa, as airlines will not allow non-nationals to board a plane to a foreign country on a one-way ticket without a visa in hand.

In fact, an Icelandair agent told me on the phone today that Icelandair would not let us board a plane to Germany with a one-way ticket unless we have already secured visas.

So, I guess we're going to have to apply for visas before we go to Germany. However, I'm afraid the visa application process may take too long (we have less than 3 months before we want to leave).

We need to buy our tickets soon, or we're going to face exorbitant fares, meaning we will need to buy our one-way tickets before we know if we'll have visas in hand or not. The Icelandair agent gave me a complicated scenario where, in addition to buying a one-way ticket from the USA to Germany, we could buy a one-way return ticket right now for a date that's within the 90 day tourist stay for Americans in Germany, then change the date for those return tickets -- allegedly without penalty. But I'm not sure I believe this/understand how this would work.

Does anyone have specific suggestions/ideas for us on what our best approach to our situation is: Wanting to be in Germany for 13 months and facing issues with one-way plane tickets, visa, etc.?

Thank you.

--Christof D-H