Can you compromise with Tiberius or Osiris and "normalise" them a bit to Tobias or Oscar? Or, what about using your DH's choice as a second name? Giving them your DH's choice but using a diminutive from day 1? Using his second name as his common name? There are lots of options.
My brother (who turns 52 this year) has been known as the diminutive of his second name since he was born. The vast majority of people don't even know his given name is James. My FiL is also known by his second name... actually not that uncommon for boys, so was my first boyfriend.
To be honest, I don't hate Tiberius, but Osiris I can't help but think of Icarus. For diminutives of both names, you could use Toby or Ozzie.
Since you didn't offer any options of your own, I just tried to make the best of your DH's preferences.
With us, our DCs have "classic" names. There is a reason behind all of DS's names (he has 3 - his great grandfather, my uncle who died in a fire when he was 16, and the friend who introduced his father and I but passed from a heart condition when he was in his early 30s) and a preference for DD's first name, but memorial for her second (no third for her).
While they are uncommon names based on current trends - they will not show up in the top 100 - they have names we are happy with.
I wish you all the best with your name search, labour and delivery.
What I recommend is that you and DH come up with a middle name, and a short list of 3 or 4 first names. Once your DS is safely in your arms, you should be able to agree on one from that list. He doesn't have to be formally named before he actually arrives - despite what you feel pressured in to.
Un-Mumsnetty hugs coming your way... I have been in your shoes. Changes of plans at this point are earth shaking.
Wishes for an easy labour and arrival are coming your way