You do have 180 days from the date of sale to complete the process.The term for those who do the exchanges is "Qualified Intermediary". 

You would not have taxable gain on your co-owner's part of the property if you received a step-up in cost basis, but would have a taxable gain if you did not receive a step-up in cost basis.However, doing a full 1031 Exchange on the entire property would defer all of the taxable gain, so I'm not sure what your Qualified Intermediary was talking about regarding your co-owner's part of the property.  

A QI (qualified intermediary) will help with your transition along with your real estate tax accountant.

Inventory is tight, but if you have an excellent advocate and intermediary working for you, they can be easy and stress free. 

Maybe if you go with a different lender since they might be using a different appraisal service (lenders no longer work directly with appraisers, there is some sort of third party intermediary) they might have a different pool. 

That  may be true in this case - cause it sure ain't your intermediary for the 1031 if that's really what they said.  

Contact your CPA and line up a "qualified intermediary".

Your 1031 Intermediary can help with that.

I've made a career of probate deals however there are often problems that don't lend themselves to a paper intermediary to solve, but rather an exoerienced investor with money, means and skill to solve problems. 

Talk to your local 1031 intermediary to understand the logistics.