You have some great feedback above from Jay and Chris, and hopefully that contact can help you out.
In your networking/loan terms search I'd reframe your ask, because what you are asking for sounds MORE risky and therefore difficult than another request. You came here to ask for 100% purchase financing on a 6 plex, but what you actually need is 20-25% down to close that seller financed transaction.
I would instead be looking for a shorter duration 2nd position note on your for sale and under contract sale property. You haven't shared all the numbers, but if that 2nd position note could be at 70% LTV and below and with a shorter say 12 month duration then it's comparatively low risk as opposed to 100% financing for a purchase. Combined with an additional pledge on the newly purchase 6-plex and your lender is in a much better position than the 100% financing.
A typical cross collateralization may also be able to accomplish what you need, but I would not be using the 100% financing language as it indicated more risk than what you're actually looking for.