Who is responsible for the tab? The person(s) who is doing the INVITING. Guests are never expected to pay their way, although I do not understand how you are inviting people to the shower from such a distance as they need to FLY IN!!!
I realize this is NOT a wedding, but the rules for WHO pays for WHAT are SIMILAR. If you refer to the link below, it clearly shows that GUESTS, and wedding attendants pay for their OWN TRAVEL COSTS. While the actual accommodations (hotel, someone's home, whatever) expenses are covered by the bride's and groom's parents (respectively), they do NOT cover TRAVEL costs!
Therefore, I cannot understand WHY YOU are covering the baby shower guests TRAVEL (flight) costs. If these guests REALLY WANT to attend, THEY should be willing AND able to cover their OWN travel costs.
But as far as the restaurant costs goes, YOU, as the "hostess" are the one responsible for covering these costs.
Now, IF you were NOT paying for the airline flights, you would have PLENTY money to cover the restaurant costs.
I really don't know how you are going to resolve this one, especially if the travel arrangements and payments have already been made.
GOOD LUCK!
Have a polite day.