My dad has the title "Seyyed" and often jokes about us being descendants of Muhammed...Does it hold any truth to it at all or has it lost its meaning over the years?

Well, both. If a historical person has living descendants the odds of being a direct descendant of that person increase drastically over time. For instance, virtually all Europeans share a common ancestor who lived about 1000 years ago.

In the case of Muhammad: "even a conservative estimate...would suggest that the number of kinsfolk [i.e. Sayyeds] is in the tens of millions."

There's also of course the genealogical issue that claims of "direct descent" are basically un-provable. Someone could have falsely claimed that descent, or some ancestor of yours could have cheated, or there could have been an adoption that didn't get recorded, etc. etc. This is common over the course of 1400 years.

I inherited a small fortune and a shitton of land in Iran, which I can only assume is "old money".

I would be extremely skeptical that this was derived in any meaningful way from being a descendant of the prophet. The title Sayyid might have granted greater social status in Iranian society, but given the number of people involved it's not as if this would have been inherited as an estate over 1400 years.