I just saw where a FTer and spouse have ten (!) successful Executive card applications approved in eleven months.
There are other card bonuses out there as well. Check and see if Barclays is still issuing US Airways MC - 50k AA miles, low required spend. Will become Aviator (AA) card soon.
Don't forget many hotel chains will allow you to accrue points for expenses made as room charges, etc. You should be able to earn HHonors points for your expenditures at the Moorea property (most, not all, properties allow this).