This is a frequently asked question in my area. I have handled many estate sales, some with multiple sibling executors and trix's. My last deal in June was 9 siblings and mom was heading for a nursing home. Feel free to contact me anytime if you would like. During these types of transactions a little more is involved with communication and so it is best to have all conversations via email or a detailed phone log noting the conversation time, date and content.
The executor is likely looking for the "best" deal as they have incurred debts and expenses on behave of the owner. They have the power to utilize any and all assets of the owner and settle all encumbrances.
So, with regard to your full price offer: When representing sellers and estate sales I try to look at the whole picture of an offer, not just the selling price. And believe it or not deposits have a big impact on most sellers. Its simple Psychology. If you decide to walk how much of a hook did you sink...or rather how big of a loss(your deposit) are you willing to walk away from. This of course is aside from agreement continguencies, like your regular home inspection and financing terms. Your seriousness is your deposit, if that makes sense.
There is a chance that because of recent Lending practices your offer was beat by a lower cash offer and in todays market with an estate sale the cash offer does offer less paperwork and a faster close.
Here is a web reference with a pretty good explanation of the executors job.
If you have any further feel free to contact me at 978/410-5248