I may not be much help in answering your question, but I think that if you don't want to lose your house, pay that bill first before paying any CC. DH and I are in a similar situation and will be filing Ch 7 BK in November(we had to wait because we had done some balance transfers earlier this year and our attorney advised waiting 6 months from the statement date) We will not be losing our house in the BK, we will keep that along with our 2 cars. It has to do with the fact that we don't have much equity in any of these things(that's how the attorney explained it)
I don't know if or when the CC would freeze your accts, are you still using the cards to meet monthly expenses like food and such? I would think they will eventually send you to collections or something of the sort but I don't know what the time frame is on that. If they have already lowered the limits and upped the monthly minimum, it may just be a matter of time before they completely close the acct.
GL to you. This is a hard situation to be in, but there are lots of ladies on here with great advice and I reccomend exploring all your options to see how to best handle this situation.