My main issue with Bitcoin is a consequence of point 2: How can Bitcoin, in the long term, possibly avoid a deflationary spiral? At a certain point, it can't inflate any more.

Deflationary spiral is a purported feature; bitcoin is designed to do that. It makes sense under certain economic models. I don't personally think it was a good choice on Satoshi's behalf, but then that's why I co-created Freicoin:

http://freico.in/

My other issue is that the maximum number of tradable units of Bitcoin is 21 million BTC / 10^-8 (smallest fraction trade-able), and 10^15 is not enough currency to run a serious global-scale economy on. But that can be fixed with additional cryptocurrencies more easily than the first problem.

There are about 15 trillion U.S. dollars in existence, the closest thing we have to a world currency. Most accounts are denominated in cents. That's only 1.5e14 units, which is very comparable. (Personally I think you will hit scalability problems long before the transaction volume is high enough to make the minimum precision a concern.)

However you definitely don't need additional crypto currencies. Use existing mechanisms to fork the transaction format and extend the precision, if necessary.