You can early exercise non-ISO options if your stock agreement allows it (also ISO but it's a little more complicated). If you also file an 83(b) election then you are indeed treated for tax purposes as if all the shares vested immediately, so if you exercise before the value of the shares exceeds your strike price then you pay no taxes until you sell the shares (or there's an acquisition or something).
As you say, the big issue with this is paying the exercise price. There's not really any way around that. If you're going to pay your employees extra money to cover the exercise price then you might as well just give them shares instead of options. Another option is to loan the money to employees. I don't know how common that is with startups.
http://www.mystockoptions.com/faq/index.cfm/catID/B7469ACD-2...
As you say, the big issue with this is paying the exercise price. There's not really any way around that. If you're going to pay your employees extra money to cover the exercise price then you might as well just give them shares instead of options. Another option is to loan the money to employees. I don't know how common that is with startups.