Credit Card Travel Insurance - Multiple Cards / Seperate Policy

Given the following:
1. Many credit cards include varying levels of travel insurance. The activation conditions vary, but some are automatic and some require an explicit opt-in.
2. Many people chose to take out a separate/explicit travel insurance policy - for the reduced excess, higher limits, more inclusions etc.
3. Many people also have multiple credit cards.
4. Most insurances have a "Multiple Policies" clause* that disclaim some/all responsibility if multiple policies apply. Seemingly without much detail.

My question is: how do the above interact?

The two main scenarios that I think are interesting/likely to actually happen:
a. I happen to meet the automatic activation conditions for two credit card policies, by eg. putting flights on one card and hotels on another.
b. I meet the automatic activation for credit card insurance and have also purchased a separate policy.

Would I end up having both providers deny, could limits be combined, etc?

Seems like this could be a potential trap as some might not even realise they're eligible from the CC side.

There's a large number of other combinations plus things like "on demand" activated polcies etc, but I'd like to understand the general principles.

WDYT?

Some example clauses:
Bankwest Credit Card:

6.If you can claim from anyone else, we will only make
up the difference
In the case that policy condition 8. Other insurance page 43
does not apply, if you can make a claim against someone in
relation to a loss or expense in respect of any of the covers
provided and they do not pay you the full amount of your claim,
we will make up the difference. You must claim from them
first

Allianz

3.1.2 What we do not cover
To the extent permitted by law, we will not
pay your claim if:
…
c] you can claim your additional travel
and accommodation expenses from
anyone else