How can I keep from getting beat out by cash buyers?

[Kevin Koffman]

I found a good multi family deal in Fort Lauderdale. But, I am bidding against cash buyers.
My problem is, I found a great lender who will finance the project for 3.375%!   my credit score is very high. That’s great, but...

This lender won’t do a cash out re-fi. So I can’t get hard money and then re-fi with this lender. I have to buy it and finance with this lender to get that rate. (Also, I’ve never borrowed from a hard money lender.) But I’m probably going to get beat out by cash buyers. The sellers realtor says the cash buyers are “pretty close” to full asking. I’m willing to pay full price, because I can get a great interest rate. The sellers don’t need a fast close but they would prefer a closing without finance contingencies as opposed to maximizing their profit. 
Any ideas?

Kevin