Most reverse exchanges are done with cash from the client or a private loan of some sort from an individual or a portfolio bank.When your old property sells you will have that cash in your account to purchase the new property. 

I have a separate positive review of this individual on BP.We spent a great deal of time formulating a strategy.

If a cash out refinance, many lenders will allow the cash out to satisfy the reserves requirement.DSCR lenders generally let you vest either individually or as an LLC.

The goal is to expand my network with likeminded individuals in the same market.   

Your 1031 will ultimately be only as good as the individuals directly assigned to your exchange.  

Also consider short term month-month leases on airbnb, renting individual rooms, month to month leases, just to get the cashflow energy flowing again.  

Renting an individual room is all but guaranteed to be cheaper than them renting a 1/1 apartment alone.

@Sufyan Minhasgoing to depend on the rules in individual buildings

In this situation, can all the partners claim mortgage payment as expense in their individual taxes (or just the partner who owns the mortgage)?

Certain expenses are all lumped together for the sake of the P&L like insurance and taxes and others like repairs and maintenance can be viewed collectively or by individual property.