Should my Swedish fiance overstay her 90-day tourist visa so we can marry here in the US instead of in Sweden?

My fiancé is a Swedish citizen; I am a US citizen. My fiancé is here on a tourist visa which expires soon. We are very much in love, and plan to marry this summer in Sweden, but don't want to risk being separated. Is it better for her to overstay her tourist visa, we marry here in the US, then apply for her permanent resident status? Our original plan was for her to fly back to Sweden this week, before her 90-day tourist visa expires, make arrangements for our marriage this summer in Sweden, return to the US in three weeks on another tourist visa, then we'd both fly back to Sweden (for our wedding) prior to the expiration of her next 90-day tourist visa. After reading about the various immigration issues, it seems that our plan could result in us being separated for a significant length of time. It also seems that we would be better off if she overstays her current 90-day tourist visa, we get married, then apply for a green card. We have established joint bank accounts, co-signed a lease, she is a beneficiary of my life insurance, and she is covered as a domestic partner family member by my employer-paid health insurance.