Since there's no way to issue a 1099 (and it would be worthless), what's the correct way to 'pay' a foreign contractor or employee without setting up a company in that country?
From my research, it seems like most countries with tax treaties with the US have exemptions for withholding. (See article 15 of the Australia / US treaty for example). In order to claim a tax treaty exemption, it looks like a foreign worker would fill out the W8-BEN form and complete section II. However, in order to fill out this form, the foreign worker needs an ITIN (international tax id number) from the Social Security Administration (SSA). And in order to get that, they have to fill out a W-7. But the W-7, for tax treaty benefits, requires they fill out the form 8223 and get a letter from the SSA saying they are ineligible for a SSN.
I've also been told the US company needs to report the income paid on form 1042 and 1042-S.
Finally, a lawyer advised me that since the entire work is being done in the foreign country and is not US sourced in any way, the income is not subject to witholding at all (regardless of tax treaty) and that a W8-BEN without part II completed is sufficient.
I'm trying to do the right thing, but the IRS is not making this easy.
This is only a partial answer; I can't help you with the US matters that are the main part of your question.
However, it's often very important to avoid any language or factual information which implies that the arrangement is between an employer and and a employee. The reason is that in other country that might place legal obligations on the employer (your company). Examples are tax withholding, pensions, social security funds etc. In Denmark the Danish courts have on several occasions held foreign companies responsible for these.
How to do this differs from country to country, but the general principle is to contract with a foreign business (possibly solely owned by the foreigner person you'd like to work with). Some general pointers are:
a lawyer advised me that since the entire work is being done in the foreign countryI don't know, but this could relate to what I'm talking about above -- buying a service on a invoice, and not an employee on a salary.