Am I understanding things correctly?
SIV requires MAC not hash. Keyed hash can be used as MAC. However, you do not have a keyed hash in your example.
Is it safe to use the same key for both keyed hash and encryption?
Normally different key should be used for MAC and encryption. Although in some cases it may be fine with same key, if MAC and encryption are different enough. For example, if you use CBC-MAC and CTR both with AES, using same key is bad. SIV defines how you derive the keys from master key.
I assume actual siv usage is a bit more than just hashing the input?
Well, again you have to use MAC.