It looks like we will just try saving. We have a Chase card that gives you 1% back on regular purchases and 5% on groceries, gas and drug stores.
I'm going to go ahead and have my husband get a business card for frequent flyer miles. We wouldn't be giving out cards to just any employees - there are two that already have them - so it wouldn't be anything new. That way we can still be earning miles for future use - perhaps not for this trip but another one.
Thanks for all your input.