Can you have 2 active directory domains with the same netbios domain name trust each other?

No this is 100% not supported or working. I have this exact scenario in my environment. Your options are domain rename or creating child domains that have trusts between each other and using resources between the child domains via a two way trust.

Another option is new domain and migrate, which might sound difficult but if it's a small amount of objects it can be done in a few hours with little downtime.

Pretty sure it's not supported scenario by Microsoft. However, you might be able to configure it if you going to use DNS name only while building cross-domain communication. I would highly suggest checking into domain rename scenario. However if you have Exchange in the domain - reinstall. Renaming a domain with Exchange in it is a prescription for permanent headache.