A HELOC or cash-out refinance would let you access funds for the down payment on a new property without needing to sell or relocate.

Any remaining funds after paying the mortgage can be kept by the property owner. 

If you are planning a hands-on project or know someone else willing to work side by side with me, I am ready to provide funding for the right deal.

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This way if 1031 proceeds are 50% of the purchase amount then 30 to 35% of funds are re-advanced out after closing keeping the 1031 exchange intact.

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@Roopesh KrishnamoorthyFinding cash flowing SFR is going to be a challenge (especially since you are looking for a primary at this point) and if you leave (H1B lottery) then do you plan to continue to fund any shortfall from India?

I made the decision to purchase a 6 unit building with those funds that will eventually cash flow $4200/month.

Lastly, don't forget to get estoppels when you close, that is the tenant signing off on the current rental amount / funds you have escrowed. 

Many are adjusting their draw funding guidelines on the fly.