I think you can achieve the goal with 5 application sprees, timed 6 months apart, starting today, before your Southwest card gets reported. For the first one, apply for the cards that don't offer high rewards so you can be approved with higher initial CL's. For the later ones, once you have already added high CL cards into your portfolio, you can shoot for better cards. Definitely throw Amex in the mix for their 61-day 3x CLI as well.
cowboyguy,
Every time you open a credit card, you gain debt allowance, which is not a good sign to creditors. Often when someone is in financial troubles, the person would try to accumulate as much debt as possible, then default. Creditors perceive new credit accounts as risk. If you apply before your new card gets reported, no one will be informed of the new card yet.
And notice that I said 5 application sprees, not 5 applications. You apply for multiple cards in each application spree. Sorry if I confused you.
Regarding your second question, I honestly have not spent much time investigating particular lenders' tendencies to match the highest credit limit from the borrower's portfolio. But many posters on here can give you their anecdotal information.
If some creditor already gave you such a high credit limit, chances are you'll get approved for similarly high limit cards. Since today is a new month, you also have one more month of credit history. Just make sure to avoid cards that are generally regarded as having tough criteria.
