Swan it is to bad the home is already an REO. You may want to keep an eye on the trustee sales at the county steps and buy straight at the trustee sale. It is a learning process but you may find yourself getting a bit better deal.
Skipping to your point, it would seem to me that if you have 1.3M liquid then you would have no problem getting financing and thus your position would not be significantly weakened if you did did come in with some in cash and some financed. I will say, any seller, (whether they are a lender or a homeowner) will give a bit more nod to the cash offer, especially if all things are equal. The problem is the difference between your offer and the “slightly” higher offers. Being the buyer it is really tough for you to get any insights into the other offers. The listing agent may tell you one thing, and it is tough to decipher if he is being square or not. I can tell you there are more then a few listing agents that have many REOs who are quite tricky to deal with.
So I know this is not a clear definitive answer but if the difference is small, a few thousand bucks, then you should be okay… If the difference is 10k, 20k something like that… well now I am not so sure… lenders are trying to get every penny they can.