When using serializable transaction SQL Server issues shared locks on read records / tables. Shared locks doesn’t allow other transactions modifying locked data (transactions will block) but it allows other transactions reading data before the transaction which issued locks start modifying data. That is the reason why the example doesn’t work – concurrent reads are allowed with shared locks until the first transaction starts modifying data.
You want isolation where select command locks the whole table exclusively for a single client. It must lock the whole table because otherwise it will not solve concurrency for inserting “the same” record. Granular control for locking records or tables by select commands is possible when using hints but you must write direct SQL queries to use them – EF has no support for that. I described approach for exclusively locking that table here but it is like creating sequential access to the table and it affects all other clients accessing this table.
If you are really sure that this operation happens just in your single method and there are not other applications using your database you can simply place the code into critical section (.NET synchronization for example with lock) and ensure on the .NET side that only single thread can access critical section. That is not so reliable solution but any playing with locks and transaction levels has a big impact on the database performance and throughput. You can combine this approach with optimistic concurrency (unique constraints, timestamps, etc).