First: never use var ts = new TransactionScope()
. Is the one liner that kills your app. Always use the explicit constructor that let you specify the isolation level. See using new TransactionScope() Considered Harmful.
Now about your question: the logic not to promote two connections in the same scope into DTC relies heavily on the driver/providers cooperating to inform the System.Transactions that the two distinct connections are capable of managing the distributed transaction just fine on their own because the resource managers involved is the same. SqlClient post SQL Server 2008 is a driver that is capable of doing this logic. The Oracle driver you use is not (and I'm not aware of any version that is, btw).
Ultimately is really really really basic: if you do not want a DTC, do not create one! Make sure you use exactly one connection in the scope. It is clearly arguable that you do not need two connections. In other words, get rid of the two separate repositories in your data model. Use only one repository for Orders, Inventory and what else what not. You are shooting yourself in the foot with them and you're asking for pixie dust solutions.
Update: Oracle driver 12c r1:
"Transaction and connection association: ODP.NET connections, by default, detach from transactions only when connection objects are closed or transaction objects are disposed"