Good to see another descendant of Öland posting on the board.
There's a genealogy group called PLF Oskarshamn, located in Oskarshamn on the mainland, opposite of Öland. They have transcribed the b/m/d records for the island. The CD costs 150 SEK + 50 SEK shipping. It's CD-4 in the series:http://www.plfoskarshamn.se/sv/cd-skivor/cd-skiva-4/
Looking at my copy, I found:
By birth year (1776): No children with the name of Carl, 1 with the name of Karl Peter. Record shows birth of 31 JUL 1776. Father is Magnus Slettberg. 9 children were unnamed out of 736 in the year.
I tried the following variations of Tornquist for the father's surname in a birth record, regardless of year.
2 children. Parishes: Högsrum & Hulterstad.
32 children. Parishes: Högby, Algutsrum, Högsrum, Hulterstad, Torslunda, Köping, Egby. Högsrum has the most births.
4 children. Parishes: Högsrum, Köping, Glömminge.
140 children. Parishes: Köping, Algutsrum, Glömminge, Runsten, Föra, Torslunda, Sandby, Löt, Persnås, Borgholm, Gårdby, Räpplinge, Vickleby, Bredsåtra, Resmo. Fairly evenly distributed throughout the parishes.
FYI: Törnqvist was used as a military name. Maybe Carl or his dad were in the navy? Soldiers db: soldat.dis.se
No records on the British side show a DOB or parent's names etc.? Any rumors of Carl being in the merchant marine?