Okay I THINK I have a connection here!
I have Philadelphia death certificates for John and Ester Bergman, as well as their daughter Sigrid, and I have John and Ester on the 1910 US census.
Sigrid, b. 3 Nov 1884, died 8 Aug 1907, address 246 Fulton St
Ester, b. 17 Dec 1862, d. 11 Apr 1912, address 246 Fulton St
John, b. 1852, per 1910 US census living with Esther at 246 Fulton St, d. 31 Jul 1914 age 61 (no birthdate listed, but approx. 1853 based on death date and age at death....also, not at the Fulton St address, but seems normal he would have moved in with someone else after his daughter and wife died)
So those are the parents of the Sweden Karl, based on the birthdates etc. from the Swedish records.
I just got Karl's marriage license from his first marriage today....he was married in 1909 to Helen Fortuna....they had one child before Helen died....Sigrid Cecilia, who is my grandmothers half sister. So I know for sure that the Karl whose license I was requesting is my correct America-Karl. And his address on the application was....246 Fulton Street!!
The same address where I can place Esther, John, and Sigrid!!
So it looks like Sweden-Karl and America-Karl are one and the same?!?!
Only thing that has me stymied is that his birthdate on the application is 28 Sept 1881, which is different than I've seen anywhere else (other records seem to have 11 Sept 1881, 11 Dec 1881, or 23 Dec 1881).
Hoping to contact the church where they were married and see if there's any further family info listed in any records.