What is the standard tag question after a statement containing "I should have ..."?

Whenever I use "I should've done _____", I like to add an extra part to the sentence looking for confirmation as in "I know, right?", where "right?" is the part asking for confirmation.

My question here is: What is the most natural way to ask for confirmation after "I should have ..."?

I should've gone to the store sooner, shouldn't've I?

I've been using "shouldn't've I?" but my girlfriend argues that that sounds weird, which it probably does. She argues that it should be "shouldn't I have?"

What tag question should I use?

The question tag for a verb phrase the starts off with an auxiliary verb followed by one or more other verbs is to invert that first auxiliary only and omit any other verbs.

• He is eating that, isn’t he? He isn’t eating that, is he?
• He was eating that, wasn’t he? He wasn’t eating that, was he?
• He has been eating that, hasn’t he? He hasn’t been eating that, has he?
• He had been eating that, hadn’t he? He hadn’t been eating that, had he?
• He should have been eating that, shouldn’t he? He shouldn’t have been eating that, should he?
  
  
• He did eat that, didn’t he? He didn’t eat that, did he?
• He has eaten that, hasn’t he? He hasn’t eaten that, has he?
• He had eaten that, hadn’t he? He hadn’t eaten that, had he?
• He can eat that, can’t he? He can’t eat that, can he?
• He will eat that, won’t he? He won’t eat that, will he?
• He could eat that, couldn’t he? He couldn’t eat that, could he?
• He should eat that, shouldn’t he? He shouldn’t eat that, should he?
• He would eat that, wouldn’t he? He wouldn’t eat that, would he?
• He might eat that, mightn’t he? He mightn’t eat that, might he?
• He must eat that, mustn’t he? He mustn’t eat that, must he?
• He could be eating that, couldn’t he? He couldn’t be eating that, could he?
• He could have eaten that, couldn’t he? He couldn’t have eaten that, could he?
• He should have eaten that, shouldn’t he? He shouldn’t have eaten that, should he?
• He would have eaten that, wouldn’t he? He wouldn’t have eaten that, would he?