Tips for handling overlapping intents? (Lex v2)

For my use case, we have defined a Greeting intent and 2 domain-specific intents - let's call them IntentA and IntentB.

The Greeting intent is trained on obvious openers like 'Hi', 'Hello', 'Hello <botname>', 'Good morning' and so forth. The bot will respond by greeting the user and informing them what the bot can help with.

For intents A and B, we are building the utterance lists with the aid of pre-bot transcripts from real users.

The issue is, many users naturally ask for intentA and intentB with a greeting phrase followed by their main intent. For example, 'Good morning, can you please help me <complete intentA>' or 'Hi there, I need to <complete intentB>'.

Since Lex does not appear to offer muiti-intent detection within a single utterance, what would be the recommended approach? Here are the strategies we're considering:

1. Train the Greeting intent on the greeting strings, and train intents A + B using phrases both with and without greeting text. (Assumption: Lex would learn that isolated greetings should match the Greeting intent, otherwise the intent-specific content should take precedence)
2. Train the Greeting intent as above, but train A + B with no greeting content. (Assumption: greeting phrases are shorter, therefore the salient portion of the user's utterance would likely be given more weight by Lex...but would this generalize if phrase lengths were equal across all 3 intents?)
3. Remove the Greeting intent and do not include greeting words in A + B training utterances. (Assumption: Greeting words in an intent would be ignored, and on their own would trigger the FallbackIntent which could be programmed to greet the user the first time & reprompt / escalate after that)
4. Explicitly treat Greeting words as stop words - would this trigger the FallbackIntent if the user says 'Hi' for example?
5. Any other options we've overlooked?

Thanks in advance!