Here are some suggestions
- Teaching oneself to sing isn't as simple as learning an instrument. There are limitations to what we can teach ourselves. Seek a teacher!
What immediately concerns me is this:
I cannot really get my throat voice that high, if I try it soon ends up sore
It is this kind of behavior that leads to injury. If your are sore, your body is telling you to stop! While I do not mean to exaggerate, you must treat your voice with care to avoid vocal nodules if you wish to become a singer. You need one on one instruction and someone to correct you while you sing.
This way one can develop good habits, posture, etc., so you can start developing on your own.
REMEMBER: your vocal chords are muscles. Singing is aerobic exercise. It involves your whole body. A "pseudo-athletic" mindset must be taken if you wish to progress (warmup, exercise, cool down, hydration, diet, etc). People who can jump right into singing are the exception, not the norm!
In combination with a vocal instructor to maintain a standard of discipline, you will see growth over time. Enjoy the journey.
- Define realistic expectations
You mentioned the following about what you dislike about your head voice and your experience:
I'm a man with no singing training and virtually no
experience singing in choirs but I do sing a fair bit (every Sunday at
church) [...] my head voice is very thin
Comparing an untrained voice to that of a professionally recorded song would deter anyone. Treasure your own voice as no one else has it! Furthermore, your head voice is secondary. Much like a saxophones altissimo, it's out of your range. While many singers have a very strong head voice, it takes a long time to develop.
Most singers go through phases where they do not enjoy the sound of their own voice. Thom Yorke of Radiohead comes to mind. Sometime following Kid A, Thom developed a sharp criticism of his own voice. It became difficult for him to listen to his voice on any recordings. You can imagine the difficulties this situation might bring. Although Thom Yorke has made a career out of singing and playing music it important to understand that everyone has challenges, even the greats.
- If seeking a teacher isn't an option, here are my recommendations for singing a difficult passage
If you feel comfortable singing the whole song, then practice only the difficult part. You will soon understand whether or not you have the ability to sing the song.
- Make a hardline decision on where to breathe between each word
- Practice going into the part with the highest note
- Practice the part with the highest note
- Practice going into the part leaving the highest note